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Artykuły w czasopismach na temat „Compressible MHD”

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Data publikacji: 6 września 2023

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1

Valdettaro, Lorenzo, and Maurice Meneguzzi. "Compressible MHD in Spherical Geometry." International Astronomical Union Colloquium 130 (1991): 80–85. http://dx.doi.org/10.1017/s0252921100079434.

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AbstractThe generation of magnetic field by a conducting, compressible fluid inside a spherical shell is studied by direct numerical simulations. A pseudo-spectral method is used in order to resolve accurately all the scales present in the problem. The range of parameters considered is the following: a unit Prandtl number, Rayleigh numbers up to 100 times critical, Taylor number 625, an aspect ratio of 2, a Mach number slightly less than 1, and pressure and temperature scale heights of the order of the thickness of the shell. A dynamo effect is observed for magnetic Prandtl numbers larger than 1. We present the properties of the turbulent flow, the role of the helicity and of the differential rotation in the enhancement of the magnetic field, and the spectral properties of the flow fields.

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2

Kowal, Grzegorz, and A. Lazarian. "Scaling Relations of Compressible MHD Turbulence." Astrophysical Journal 666, no. 2 (2007): L69—L72. http://dx.doi.org/10.1086/521788.

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3

Zank, G. P., and W. H. Matthaeus. "The equations of reduced magnetohydrodynamics." Journal of Plasma Physics 48, no. 1 (1992): 85–100. http://dx.doi.org/10.1017/s002237780001638x.

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The equations of high- and low-beta reduced magnetohydrodynamics (RMHD) are considered anew in order to elucidate the relationship between compressible MHD and RMHD and also to distinguish RMHD from recently developed models of nearly incompressible MHD. Our results, summarized in two theorems, provide the conditions under which RMHD represents a valid reduction of compressible MHD. The equations for low-beta RMHD and high-beta RMHD are shown to be identical. Furthermore, as a direct consequence of our analysis, the conditions under which both two-dimensional incompressible MHD (in terms of the spatial co-ordinates as well as the fluid variables) and 2½ dimensional incompressible MHD (i.e. only two-dimensional in the spatial co-ordinates) represent a valid reduction of three-dimensional compressible MHD are also formulated. It is found that the elimination of all high-frequency and long-wavelength modes from the magneto-fluid reduces the fully compressible MHD equations to either two-dimensional incompressible MHD in the plasma beta (β) limit β ≪ 1, or 2½-dimensional incompressible MHD for β ≈ 1. Our approach clarifies several inconsistencies to be found in previous investigations in that the reduction is exact. Our results and analysis are expected to be of interest for plasma fusion and space and solar physics.

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4

Chanteur, G. "Localized Alfvénic solutions of nondissipative and compressible MHD." Nonlinear Processes in Geophysics 6, no. 3/4 (1999): 145–48. http://dx.doi.org/10.5194/npg-6-145-1999.

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Abstract. Alfvénic solutions of nondissipative MHD are entirely determined by their magnetic configuration. With the supplementary assumption of incompressibility any solenoidal field can be used to construct an Alfvénic solution. It is demonstrated that for nondissipative and compressible MHD the energy equation constrains the magnetic field of Alfvénic solutions to have a constant strength along field lines. Some topological solitons known in nondissipative and incompressible MHD do not have this property. New localized axisymmetric Alfvénic solutions of nondissipative and compressible MHD are explicitly constructed.

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5

WISNIEWSKI, MARTINA, RALF KISSMANN, and FELIX SPANIER. "Turbulence evolution in MHD plasmas." Journal of Plasma Physics 79, no. 5 (2013): 597–612. http://dx.doi.org/10.1017/s0022377813000147.

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AbstractTurbulence in the interstellar medium has been an active field of research in the last decade. Numerical simulations are the tool of choice in most cases. However, while there are a number of simulations on the market, some questions have not been answered finally. In this paper, we examine the influence of compressible and incompressible driving on the evolution of turbulent spectra in a number of possible interstellar medium scenarios. We conclude that the driving has an influence not only on the ratio of compressible to incompressible component but also on the anisotropy of turbulence.

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6

王, 帅. "The Important Estimates for Compressible MHD Equations." Pure Mathematics 12, no. 08 (2022): 1305–11. http://dx.doi.org/10.12677/pm.2022.128143.

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7

Hesse, Michael, Joachim Birn, and Seiji Zenitani. "Magnetic reconnection in a compressible MHD plasma." Physics of Plasmas 18, no. 4 (2011): 042104. http://dx.doi.org/10.1063/1.3581077.

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8

Lu, Ming, Yi Du, and Zheng-an Yao. "Blow-up criterion for compressible MHD equations." Journal of Mathematical Analysis and Applications 379, no. 1 (2011): 425–38. http://dx.doi.org/10.1016/j.jmaa.2011.01.043.

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9

Cho, Jungyeon, and A. Lazarian. "Generation of compressible modes in MHD turbulence." Theoretical and Computational Fluid Dynamics 19, no. 2 (2005): 127–57. http://dx.doi.org/10.1007/s00162-004-0157-x.

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10

Oughton, S., W. H. Matthaeus, Minping Wan, and Tulasi Parashar. "Variance anisotropy in compressible 3-D MHD." Journal of Geophysical Research: Space Physics 121, no. 6 (2016): 5041–54. http://dx.doi.org/10.1002/2016ja022496.

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11

Andrés, N., R. Bandyopadhyay, D. J. McComas, et al. "Observation of Turbulent Magnetohydrodynamic Cascade in the Jovian Magnetosheath." Astrophysical Journal 945, no. 1 (2023): 8. http://dx.doi.org/10.3847/1538-4357/acb7e0.

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Abstract We present the first estimation of the energy cascade rate in Jupiter’s magnetosheath (MS). We use in situ observations from the Jovian Auroral Distributions Experiment and the magnetometer investigation instruments on board the Juno spacecraft, in concert with two recent compressible models, to investigate the cascade rate in the magnetohydrodynamic (MHD) scales. While a high level of compressible density fluctuations is observed in the Jovian MS, a constant energy flux exists in the MHD inertial range. The compressible isothermal and polytropic energy cascade rates increase in the MHD range when density fluctuations are present. We find that the energy cascade rate in Jupiter’s magnetosheath is at least 2 orders of magnitude (100 times) smaller than the corresponding typical value in the Earth’s magnetosheath.

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12

Zhao, S. Q., Huirong Yan, Terry Z. Liu, Mingzhe Liu, and Mijie Shi. "Analysis of Magnetohydrodynamic Perturbations in the Radial-field Solar Wind from Parker Solar Probe Observations." Astrophysical Journal 923, no. 2 (2021): 253. http://dx.doi.org/10.3847/1538-4357/ac2ffe.

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Abstract We report analysis of sub-Alfvénic magnetohydrodynamic (MHD) perturbations in the low-β radial-field solar wind employing the Parker Solar Probe spacecraft data from 2018 October 31 to November 12. We calculate wavevectors using the singular value decomposition method and separate MHD perturbations into three eigenmodes (Alfvén, fast, and slow modes) to explore the properties of sub-Alfvénic perturbations and the role of compressible perturbations in solar wind heating. The MHD perturbations show a high degree of Alfvénicity in the radial-field solar wind, with the energy fraction of Alfvén modes dominating (∼45%–83%) over those of fast modes (∼16%–43%) and slow modes (∼1%–19%). We present a detailed analysis of a representative event on 2018 November 10. Observations show that fast modes dominate magnetic compressibility, whereas slow modes dominate density compressibility. The energy damping rate of compressible modes is comparable to the heating rate, suggesting the collisionless damping of compressible modes could be significant for solar wind heating. These results are valuable for further studies of the imbalanced turbulence near the Sun and possible heating effects of compressible modes at MHD scales in low-β plasma.

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13

Cui, Xiufang, Shengxin Li, and Feng Xie. "Uniform regularity estimates and inviscid limit for the compressible non-resistive magnetohydrodynamics system." Nonlinearity 36, no. 1 (2022): 354–400. http://dx.doi.org/10.1088/1361-6544/aca511.

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Abstract We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the assumption that the initial magnetic field is transverse to the boundary, the uniform conormal energy estimates are established for the solutions to compressible MHD equations with respect to the small viscosity coefficient. As a direct consequence, we proved the inviscid limit of solutions from viscous MHD systems to the ideal MHD systems in L ∞ sense by some compact arguments. Our results show that the transverse magnetic field near the boundary can prevent the strong boundary layers from occurring.

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14

Magyar, N., T. Van Doorsselaere, and M. Goossens. "The Nature of Elsässer Variables in Compressible MHD." Astrophysical Journal 873, no. 1 (2019): 56. http://dx.doi.org/10.3847/1538-4357/ab04a7.

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15

Matsumoto, Takuma. "Full compressible 3D MHD simulation of solar wind." Monthly Notices of the Royal Astronomical Society 500, no. 4 (2020): 4779–87. http://dx.doi.org/10.1093/mnras/staa3533.

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ABSTRACT Identifying the heating mechanisms of the solar corona and the driving mechanisms of solar wind are key challenges in understanding solar physics. A full three-dimensional compressible magnetohydrodynamic (MHD) simulation was conducted to distinguish between the heating mechanisms in the fast solar wind above the open field region. Our simulation describes the evolution of the Alfvénic waves, which includes the compressible effects from the photosphere to the heliospheric distance s of 27 solar radii (R⊙). The hot corona and fast solar wind were reproduced simultaneously due to the dissipation of the Alfvén waves. The inclusion of the transition region and lower atmosphere enabled us to derive the solar mass-loss rate for the first time by performing a full three-dimensional compressible MHD simulation. The Alfvén turbulence was determined to be the dominant heating mechanism in the solar wind acceleration region (s &gt; 1.3 R⊙), as suggested by previous solar wind models. In addition, shock formation and phase mixing are important below the lower transition region (s &lt; 1.03 R⊙) as well.

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16

Radwan, Ahmed E. "MHD stability of a gravitating compressible fluid cylinder." Physica Scripta 39, no. 2 (1989): 284–88. http://dx.doi.org/10.1088/0031-8949/39/2/019.

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17

Meng, Qiu. "Generalized solutions to time-discretized compressible MHD equations." Zeitschrift für angewandte Mathematik und Physik 66, no. 3 (2014): 819–32. http://dx.doi.org/10.1007/s00033-014-0436-3.

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18

Nataraja, H. R., M. L. Mittal, and B. Nageswara Rao. "Laminar MHD compressible boundary layer at a wedge." International Journal of Engineering Science 24, no. 8 (1986): 1303–10. http://dx.doi.org/10.1016/0020-7225(86)90059-5.

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19

Naidu, V. G., K. S. Rao, M. L. Mittal, and B. Nageswara Rao. "Laminar compressible MHD (magneto hydro dynamic) boundary layers." Forschung im Ingenieurwesen 55, no. 6 (1989): 196–98. http://dx.doi.org/10.1007/bf02561035.

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20

Fan, Jishan, and Yong Zhou. "Uniform regularity of fully compressible Hall-MHD systems." Electronic Journal of Differential Equations 2021, no. 01-104 (2021): 17. http://dx.doi.org/10.58997/ejde.2021.17.

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In this article we study a fully compressible Hall-MHD system. These equations include shear viscosity, bulk viscosity of the flow, and heat conductivity and resistivity coefficients. We prove uniform regularity estimates. For more information see https://ejde.math.txstate.edu/Volumes/2021/17/abstr.html

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21

Li, Zilai, Huaqiao Wang, and Yulin Ye. "On non-resistive limit of 1D MHD equations with no vacuum at infinity." Advances in Nonlinear Analysis 11, no. 1 (2021): 702–25. http://dx.doi.org/10.1515/anona-2021-0209.

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Abstract In this paper, the Cauchy problem for the one-dimensional compressible isentropic magnetohydrodynamic (MHD) equations with no vacuum at infinity is considered, but the initial vacuum can be permitted inside the region. By deriving a priori ν (resistivity coefficient)-independent estimates, we establish the non-resistive limit of the global strong solutions with large initial data. Moreover, as a by-product, the global well-posedness of strong solutions for the compressible resistive MHD equations is also established.

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22

Xie, Feng, and Christian Klingenberg. "A limit problem for three-dimensional ideal compressible radiation magneto-hydrodynamics." Analysis and Applications 16, no. 01 (2017): 85–102. http://dx.doi.org/10.1142/s0219530516500238.

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General radiation magnetic hydrodynamics models include two main parts that are coupled: one part is the macroscopic magnetic fluid part, which is governed by the ideal compressible magnetohydrodynamic (MHD) equations with additional radiation terms; another part is the radiation field, which is described by a transfer equation. It is well known that in radiation hydrodynamics without a magnetic field there are two physical approximations: one is the so-called P1 approximation and the other is the so-called gray approximation. Starting out with a general radiation MHD model one can derive the so-called MHD-P1 approximation model. In this paper, we study the non-relativistic type limit for this MHD-P1 approximation model since the speed of light is much larger than the speed of the macroscopic fluid. This way we achieve a rigorous derivation of a widely used macroscopic model in radiation magnetohydrodynamics.

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23

Erdélyi, R., M. Goossens, and S. Poedts. "Linear Visco-Resistive Computations of Magnetohydrodynamic Waves: I. The Code and Test Cases." International Astronomical Union Colloquium 144 (1994): 503–5. http://dx.doi.org/10.1017/s0252921100025926.

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AbstractThe stationary state of resonant absorption of linear, MHD waves in cylindrical magnetic flux tubes is studied in viscous, compressible MHD with a numerical code using finite element discretization. The full viscosity tensor with the five viscosity coefficients as given by Braginskii is included in the analysis. Our computations reproduce the absorption rates obtained by Lou in scalar viscous MHD and Goossens and Poedts in resistive MHD, which guarantee the numerical accuracy of the tensorial viscous MHD code.

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24

Montagud-Camps, Victor, František Němec, Jana Šafránková, et al. "Flattening of the Density Spectrum in Compressible Hall-MHD Simulations." Atmosphere 12, no. 9 (2021): 1162. http://dx.doi.org/10.3390/atmos12091162.

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Observations of proton density fluctuations of the solar wind at 1 au have shown the presence of a decade-long transition region of the density spectrum above sub-ion scales, characterized by a flattening of the spectral slope. We use the proton density fluctuations data collected by the BMSW instrument on-board the Spektr-R satellite in order to delimit the plasma parameters under which the transition region can be observed. Under similar plasma conditions to those in observations, we carry out 3D compressible magnetohydrodynamics (MHD) and Hall-MHD numerical simulations and find that Hall physics is necessary to generate the transition region. The analysis of the kω power spectrum in the Hall-MHD simulation indicates that the flattening of the density spectrum is associated with fluctuations having frequencies smaller than the ion cyclotron frequency.

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25

Shi, Kunlong, and Tong Tang. "Uniform regularity for the nonisentropic MHD system." Glasnik Matematicki 57, no. 2 (2022): 281–90. http://dx.doi.org/10.3336/gm.57.2.08.

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In this work, we prove the uniform regularity of smooth solutions to the full compressible MHD system in \(\mathbb{T}^3\). Here our result is obtained by using the bilinear commutator and product estimates.

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26

Liu, Hairong, Tao Luo, and Hua Zhong. "Global solutions to an initial boundary problem for the compressible 3D MHD equations with Navier-slip and perfectly conducting boundary conditions in exterior domains." Nonlinearity 35, no. 12 (2022): 6156–203. http://dx.doi.org/10.1088/1361-6544/ac98eb.

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Abstract An initial boundary value problem for compressible magnetohydrodynamics (MHD) is considered on an exterior domain (with the vanishing first Betti number) in R 3 in this paper. The global existence of smooth solutions near a given constant state for compressible MHD with the boundary conditions of Navier-slip for the velocity filed and perfect conduction for the magnetic field is established. Moreover the explicit decay rate is given. In particular, the results obtained in this paper also imply the global existence of classical solutions for the full compressible Navier–Stokes equations with Navier-slip boundary conditions on exterior domains in three dimensions, which was not available in literature prior to the work in this paper, to the best of knowledge of the authors’.

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27

Lu, Ming, Yi Du, and Zheng-An Yao. "Blow-up phenomena for the 3D compressible MHD equations." Discrete & Continuous Dynamical Systems - A 32, no. 5 (2012): 1835–55. http://dx.doi.org/10.3934/dcds.2012.32.1835.

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28

Balsara, Dinshaw S., Rakesh Kumar, and Praveen Chandrashekar. "Globally divergence-free DG scheme for ideal compressible MHD." Communications in Applied Mathematics and Computational Science 16, no. 1 (2021): 59–98. http://dx.doi.org/10.2140/camcos.2021.16.59.

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29

Zhou, Yanping, Xuemei Deng, Qunyi Bie, and Lingping Kang. "Energy conservation for the compressible ideal Hall-MHD equations." AIMS Mathematics 7, no. 9 (2022): 17150–65. http://dx.doi.org/10.3934/math.2022944.

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<abstract><p>In this paper, we study the regularity and energy conservation of the weak solutions for compressible ideal Hall-magnetohydrodynamic (Hall-MHD) system, where $ (t, x)\in(0, T)\times {\mathbb{T}}^d(d\geq\; 1) $. By exploring the special structure of the nonlinear terms in the model, we obtain the sufficient conditions for the regularity of the weak solutions for energy conservation. Our main strategy relies on commutator estimates.</p></abstract>

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30

CALLY, P. S., and S. T. MADDISON. "A modal view of oscillations in inhomogeneous compressible MHD." Journal of Plasma Physics 57, no. 3 (1997): 591–609. http://dx.doi.org/10.1017/s0022377897005448.

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31

L. Azwz, Shimaa. "HYDROMAGNETIC STABILITY OF STREAMING COMPRESSIBLE CYLINDER PERVADED BY MAGNETIC FIELD." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 12, no. 4 (2014): 3421–27. http://dx.doi.org/10.24297/ijct.v12i4.3184.

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The Stability of MHD compressible streaming fluid cylinder of radius endowed with surface tension and pervaded by axial magnetic field has been developed. The stability criterion is established in general form. The model is capillary unstable only in the axisymmetric mode m=0, the electromagnetic forces acting interior and exterior the fluid cylinder are stabilizing and the MHD stability is destabilizing for small wave length. In the latter case the instability shrinks with increasing the magnetic intensity. However the compressibility has a stabilizing tendency.

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32

Kawazura, Y. "CALLIOPE: Pseudospectral Shearing Magnetohydrodynamics Code with a Pencil Decomposition." Astrophysical Journal 928, no. 2 (2022): 113. http://dx.doi.org/10.3847/1538-4357/ac4f63.

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Abstract The pseudospectral method is a highly accurate numerical scheme suitable for turbulence simulations. We have developed an open-source pseudospectral code, calliope, which adopts the P3DFFT library to perform a fast Fourier transform with the two-dimensional (pencil) decomposition of numerical grids. calliope can solve incompressible magnetohydrodynamics (MHD), isothermal compressible MHD, and rotational reduced MHD with parallel computation using very large numbers of cores (>105 cores for 20483 grids). The code can also solve for local magnetorotational turbulence in a shearing frame using the remapping method. calliope is currently the only pseudospectral code that can compute magnetorotational turbulence using pencil-domain decomposition. This paper presents the numerical scheme of calliope and the results of linear and nonlinear numerical tests, including compressible local magnetorotational turbulence with the largest grid number reported to date.

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33

Lu, Li. "One new blow-up criterion for the two-dimensional full compressible magnetohydrodynamic equations." AIMS Mathematics 8, no. 7 (2023): 15876–91. http://dx.doi.org/10.3934/math.2023810.

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<abstract><p>This paper concerns the blow-up criterion for two-dimensional (2D) viscous, compressible, and heat conducting magnetohydrodynamic(MHD) flows. When the magnetic field $ H $ satisfies the perfect conducting boundary condition $ H\cdot n = \mbox{curl} H = 0 $, we prove that for the initial boundary value problem of the two-dimensional full compressible MHD flows with initial density allowed to vanish, the strong solution exists globally provided $ \|H\|_{L^\infty(0, T; \; L^b)}+\| {{\rm{div }}} u\|_{L^1(0, T; \; L^\infty)} &lt; \infty $ for any $ b &gt; 2 $.</p></abstract>

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34

Sun, Jianzhu, Huasong Jiang, and Caochuan Ma. "Local well-posedness for a compressible full MHD-P1 approximate model arising in radiation MHD." Journal of Mathematical Analysis and Applications 459, no. 2 (2018): 1138–48. http://dx.doi.org/10.1016/j.jmaa.2017.11.030.

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35

Galtier, S., S. V. Nazarenko, and A. C. Newell. "On wave turbulence in MHD." Nonlinear Processes in Geophysics 8, no. 3 (2001): 141–50. http://dx.doi.org/10.5194/npg-8-141-2001.

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Abstract. We describe the fundamental differences between weak (wave) turbulence in incompressible and weakly compressible MHD at the level of three-wave interactions. The main difference is in the structure of the resonant manifolds and the mechanisms of redistribution of spectral densities along the applied magnetic field B0. Similar to pure acoustic waves, a three-wave resonance between collinear wave vectors is observed but, in addition, we also have a resonance through tilted planes and spheres. The properties of resonances and their consequences for the asymptotics are also discussed.

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36

Čadež, V. M., and V. K. Okretič. "Leakage of MHD surface waves in structured media." Journal of Plasma Physics 41, no. 1 (1989): 23–30. http://dx.doi.org/10.1017/s0022377800013611.

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Surface-wave propagation along a double step is investigated within ideal compressible MHD. The occurrence of surface-wave leakage is emphasized and the relevant conditions are discussed. A numerical example is presented to illustrate the process.

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37

Brodiano, M., P. Dmitruk, and N. Andrés. "A statistical study of the compressible energy cascade rate in solar wind turbulence: Parker solar probe observations." Physics of Plasmas 30, no. 3 (2023): 032903. http://dx.doi.org/10.1063/5.0109379.

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We investigated incompressible and compressible magnetohydrodynamic (MHD) energy cascade rates in the solar wind at different heliocentric distances. We used in situ magnetic field and plasma observations provided by the Parker Solar Probe mission and exact relations in fully developed turbulence. To estimate the compressible cascade rate, we applied two recent exact relations for compressible isothermal and polytropic MHD turbulence, respectively. Our observational results show a clear increase in the absolute value of the compressible and incompressible cascade rates as we get closer to the Sun. Moreover, we obtained an increase in both isothermal and polytropic cascade rates with respect to the incompressible case as compressibility increases in the plasma. Further discussion about the relation between the compressibility and the heliocentric distance is carried out. Furthermore, we compared both exact relations as compressibility increases in the solar wind, and although we note a slight trend to observe larger cascades using a polytropic closure, we obtained essentially the same cascade rate in the range of compressibility observed. Finally, we investigated the signed incompressible and compressible energy cascade rates and its connection with the real cascade rate.

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38

SHAIKH, DASTGEER, and P. K. SHUKŁA. "Nonlinear electromagnetic wave interactions in Hall–MHD plasmas." Journal of Plasma Physics 76, no. 6 (2010): 893–901. http://dx.doi.org/10.1017/s0022377810000486.

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AbstractWe have developed a massively parallelized fully three-dimensional (3D) compressible Hall–magnetohydrodynamic (MHD) code to investigate inertial range electromagnetic wave cascades and dissipative processes in the regime, where characteristic length scales associated with plasma fluctuations are smaller than ion gyroradii. Such regime is ubiquitously present in the solar wind and many other collisionless space plasmas. Particularly, in the solar wind, the high time resolution databases depict a spectral break near the end of the 5/3 spectrum that corresponds to a high-frequency regime where the electromagnetic turbulent cascades cannot be explained by the usual MHD models. This refers to a second inertial range, where turbulent cascades follow a k−7/3 (where k is a wavenumber) spectrum in which the characteristic electromagnetic fluctuations evolve typically on kinetic Alfvén time scales. In this paper, we describe results from our 3D compressible Hall–MHD simulations that explain the observed k−7/3 spectrum in the solar wind plasma, energy cascade, anisotropy, and other spectral features.

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Tao, Qiang, and Canze Zhu. "Global well-posedness of the full compressible Hall-MHD equations." Advances in Nonlinear Analysis 10, no. 1 (2021): 1235–54. http://dx.doi.org/10.1515/anona-2020-0178.

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Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

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Lu, Ming, Yi Du, Zheng-An Yao, and Zujin Zhang. "A blow-up criterion for the 3D compressible MHD equations." Communications on Pure & Applied Analysis 11, no. 3 (2012): 1167–83. http://dx.doi.org/10.3934/cpaa.2012.11.1167.

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Trebeschi, Paola. "On the slightly compressible MHD system in the half-plane." Communications on Pure & Applied Analysis 3, no. 1 (2004): 97–113. http://dx.doi.org/10.3934/cpaa.2004.3.97.

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Shuchao, Duan, and Ma Zhiwei. "Spectral Properties of MHD Turbulence in 2.5-Dimensional Compressible Plasmas." Plasma Science and Technology 11, no. 2 (2009): 146–51. http://dx.doi.org/10.1088/1009-0630/11/2/04.

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Yuan, Baoquan, and Xiaokui Zhao. "Blow-up Criteria for the 2D Full Compressible MHD system." Applicable Analysis 93, no. 7 (2013): 1339–57. http://dx.doi.org/10.1080/00036811.2013.831076.

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Pan, Xinghong, and Lu Zhu. "The incompressible limit for compressible MHD equations inLptype critical spaces." Nonlinear Analysis 170 (May 2018): 21–46. http://dx.doi.org/10.1016/j.na.2017.12.015.

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Charlton, L. A., J. A. Holmes, V. E. Lynch, B. A. Carreras, and T. C. Hender. "Compressible linear and nonlinear resistive MHD calculations in toroidal geometry." Journal of Computational Physics 86, no. 2 (1990): 270–93. http://dx.doi.org/10.1016/0021-9991(90)90102-7.

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Erdélyi, Robert, and Viktor Fedun. "Linear MHD Sausage Waves in Compressible Magnetically Twisted Flux Tubes." Solar Physics 246, no. 1 (2007): 101–18. http://dx.doi.org/10.1007/s11207-007-9022-6.

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Chernyshov, Aleksandr A., Kirill V. Karelsky, and Arakel S. Petrosyan. "Assessment of Subgrid-Scale Models for Decaying Compressible MHD Turbulence." Flow, Turbulence and Combustion 80, no. 1 (2007): 21–35. http://dx.doi.org/10.1007/s10494-007-9100-8.

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Li, Zhong-Zheng, Juan-Fang Han, Fang-Ping Wang, Zheng-Wu Chen, Li-Qiang Xie, and Wen-Shan Duan. "Linear and nonlinear Alfvén wave propagation in compressible MHD plasmas." Modern Physics Letters B 34, no. 25 (2020): 2050272. http://dx.doi.org/10.1142/s0217984920502723.

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Evolution of both low-frequency harmonic Alfvén wave train and Alfvén solitary wave is studied by using the compressible MHD fluid model. A critical point is found at which linear wave theory should be replaced by a nonlinear one. A small, but finite amplitude Alfvén solitary wave is numerically found. The head-on collision between an Alfvén wave train and an Alfvén solitary wave is also numerically investigated. An interesting result is that there is no phase shift for both colliding waves which is different from that between two KdV solitary waves.

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Lazarian, A., and J. Cho. "Basic Properties of Compressible MHD Turbulence: Implications for Molecular Clouds." Astrophysics and Space Science 292, no. 1-4 (2004): 29–43. http://dx.doi.org/10.1023/b:astr.0000044998.74603.91.

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Xenos, M., S. Dimas, and N. Kafoussias. "MHD compressible turbulent boundary-layer flow with adverse pressure gradient." Acta Mechanica 177, no. 1-4 (2005): 171–90. http://dx.doi.org/10.1007/s00707-005-0221-7.

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