Relevant bibliographies by topics / Strichartz estimates

Academic literature on the topic 'Strichartz estimates'

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Published: 4 June 2021
Last updated: 7 February 2022

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Journal articles on the topic "Strichartz estimates"

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Keel, Markus Aloysius, and Terence Tao. "Endpoint Strichartz estimates." American Journal of Mathematics 120, no. 5 (1998): 955–80. http://dx.doi.org/10.1353/ajm.1998.0039.

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FOSCHI, DAMIANO. "INHOMOGENEOUS STRICHARTZ ESTIMATES." Journal of Hyperbolic Differential Equations 02, no. 01 (March 2005): 1–24. http://dx.doi.org/10.1142/s0219891605000361.

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We look for the optimal range of Lebesque exponents for which inhomogeneous Strichartz estimates are valid. It is known that this range is larger than the one given by admissible exponents for homogeneous estimates. We prove inhomogeneous estimates in this larger range adopting the abstract setting and interpolation techniques already used by Keel and Tao for the endpoint case of the homogeneous estimates. Applications to Schrödinger equations are given, which extend previous work by Kato.
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Schippa, Robert. "Generalized inhomogeneous Strichartz estimates." Discrete & Continuous Dynamical Systems - A 37, no. 6 (2017): 3387–410. http://dx.doi.org/10.3934/dcds.2017143.

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Alazard, Thomas, Nicolas Burq, and Claude Zuily. "Strichartz estimates for water waves." Annales scientifiques de l'École normale supérieure 44, no. 5 (2011): 855–903. http://dx.doi.org/10.24033/asens.2156.

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Jiang, Jin-Cheng, Chengbo Wang, and Xin Yu. "Generalized and weighted Strichartz estimates." Communications on Pure and Applied Analysis 11, no. 5 (March 2012): 1723–52. http://dx.doi.org/10.3934/cpaa.2012.11.1723.

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Cho, Yonggeun, and Sanghyuk Lee. "Strichartz estimates in spherical coordinates." Indiana University Mathematics Journal 62, no. 3 (2013): 991–1020. http://dx.doi.org/10.1512/iumj.2013.62.4970.

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Schippa, Robert. "Sharp Strichartz estimates in spherical coordinates." Communications on Pure & Applied Analysis 16, no. 6 (2017): 2047–51. http://dx.doi.org/10.3934/cpaa.2017100.

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Chen, Gong. "Strichartz estimates for charge transfer models." Discrete & Continuous Dynamical Systems - A 37, no. 3 (2017): 1201–26. http://dx.doi.org/10.3934/dcds.2017050.

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Hong, Younghun, and Changhun Yang. "Uniform Strichartz estimates on the lattice." Discrete & Continuous Dynamical Systems - A 39, no. 6 (2019): 3239–64. http://dx.doi.org/10.3934/dcds.2019134.

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CORDERO, ELENA, and DAVIDE ZUCCO. "Strichartz Estimates for the Schrödinger Equation." Cubo (Temuco) 12, no. 3 (2010): 213–39. http://dx.doi.org/10.4067/s0719-06462010000300014.

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Dissertations / Theses on the topic "Strichartz estimates"

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Dinh, Van Duong. "Strichartz estimates and the nonlinear Schrödinger-type equations." Thesis, Toulouse 3, 2018. http://www.theses.fr/2018TOU30247/document.

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Cette thèse est consacrée à l'étude des aspects linéaires et non-linéaires des équations de type Schrödinger [ i partial_t u + |nabla|^sigma u = F, quad |nabla| = sqrt {-Delta}, quad sigma in (0, infty).] Quand $sigma = 2$, il s'agit de l'équation de Schrödinger bien connue dans de nombreux contextes physiques tels que la mécanique quantique, l'optique non-linéaire, la théorie des champs quantiques et la théorie de Hartree-Fock. Quand $sigma in (0,2) backslash {1}$, c'est l'équation Schrödinger fractionnaire, qui a été découverte par Laskin (voir par exemple cite{Laskin2000} et cite{Laskin2002}) en lien avec l'extension de l'intégrale de Feynman, des chemins quantiques de type brownien à ceux de Lévy. Cette équation apparaît également dans des modèles de vagues (voir par exemple cite{IonescuPusateri} et cite{Nguyen}). Quand $sigma = 1$, c'est l'équation des demi-ondes qui apparaît dans des modèles de vagues (voir cite{IonescuPusateri}) et dans l'effondrement gravitationnel (voir cite{ElgartSchlein}, cite{FrohlichLenzmann}). Quand $sigma = 4$, c'est l'équation Schrödinger du quatrième ordre ou biharmonique introduite par Karpman cite{Karpman} et par Karpman-Shagalov cite{KarpmanShagalov} pour prendre en compte le rôle de la dispersion du quatrième ordre dans la propagation d'un faisceau laser intense dans un milieu massif avec non-linéarité de Kerr. Cette thèse est divisée en deux parties. La première partie étudie les estimations de Strichartz pour des équations de type Schrödinger sur des variétés comprenant l'espace plat euclidien, les variétés compactes sans bord et les variétés asymptotiquement euclidiennes. Ces estimations de Strichartz sont utiles pour l'étude de l'équations dispersives non-linéaire à régularité basse. La seconde partie concerne l'étude des aspects non-linéaires tels que les caractères localement puis globalement bien posés sous l'espace d'énergie, ainsi que l'explosion de solutions peu régulières pour des équations non-linéaires de type Schrödinger. [...]
This dissertation is devoted to the study of linear and nonlinear aspects of the Schrödinger-type equations [ i partial_t u + |nabla|^sigma u = F, quad |nabla| = sqrt {-Delta}, quad sigma in (0, infty).] When $sigma = 2$, it is the well-known Schrödinger equation arising in many physical contexts such as quantum mechanics, nonlinear optics, quantum field theory and Hartree-Fock theory. When $sigma in (0,2) backslash {1}$, it is the fractional Schrödinger equation, which was discovered by Laskin (see e.g. cite{Laskin2000} and cite{Laskin2002}) owing to the extension of the Feynman path integral, from the Brownian-like to Lévy-like quantum mechanical paths. This equation also appears in the water waves model (see e.g. cite{IonescuPusateri} and cite{Nguyen}). When $sigma = 1$, it is the half-wave equation which arises in water waves model (see cite{IonescuPusateri}) and in gravitational collapse (see cite{ElgartSchlein}, cite{FrohlichLenzmann}). When $sigma =4$, it is the fourth-order or biharmonic Schrödinger equation introduced by Karpman cite {Karpman} and by Karpman-Shagalov cite{KarpmanShagalov} taking into account the role of small fourth-order dispersion term in the propagation of intense laser beam in a bulk medium with Kerr nonlinearity. This thesis is divided into two parts. The first part studies Strichartz estimates for Schrödinger-type equations on manifolds including the flat Euclidean space, compact manifolds without boundary and asymptotically Euclidean manifolds. These Strichartz estimates are known to be useful in the study of nonlinear dispersive equation at low regularity. The second part concerns the study of nonlinear aspects such as local well-posedness, global well-posedness below the energy space and blowup of rough solutions for nonlinear Schrödinger-type equations.[...]
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Ovcharov, Evgeni Y. "Global regularity of nonlinear dispersive equations and Strichartz estimates." Thesis, University of Edinburgh, 2010. http://hdl.handle.net/1842/4600.

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The main part of the thesis is set to review and extend the theory of the so called Strichartztype estimates. We present a new viewpoint on the subject according to which our primary goal is the study of the (endpoint) inhomogeneous Strichartz estimates. This is based on our result that the class of all homogeneous Strichartz estimates (understood in the wider sense of homogeneous estimates for data which might be outside the energy class) are equivalent to certain types of endpoint inhomogeneous Strichartz estimates. We present our arguments in the abstract setting but make explicit derivations for the most important dispersive equations like the Schr¨odinger , wave, Dirac, Klein-Gordon and their generalizations. Thus some of the explicit estimates appear for the first time although their proofs might be based on ideas that are known in other special contexts. We present also several new advancements on well-known open problems related to the Strichartz estimates. One problem we pay a special attention is the endpoint homogeneous Strichartz estimate for the kinetic transport equation (and its generalization to estimates with vector-valued norms.) For example, this problem was considered by Keel and Tao [30], but at the time the authors were not able to resolve it. We also fall short of resolving that problem but instead we prove a weaker version of it that can be useful for applications. Moreover, we also make a conjecture and give a counterexample related to that problem which might be useful for its potential resolution. Related to the latter is the fact that we now primarily use complex interpolation in the proof of the homogeneous and the inhomogeneous Strichartz estimates, which produces more natural norms in the vector-valued and the abstract setting compared to the real method of interpolation employed in earlier works. Another important direction of the thesis is to study the range of validity of the Strichartz estimates for the kinetic transport equation which requires a separate and more delicate approach due to its vector-valued dispersive inequality and a special invariance property. We produce an almost optimal range of estimates for that equation. It is an interesting fact that the failure of certain endpoint estimates with L∞ or L1-space norms can be shown on characteristics of Besicovitch sets. With regard to applications of these estimates we demonstrate for the first time in the context of a nonlinear kinetic system (the Othmer-Dunbar-Alt kinetic model of bacterial chemotaxis) that its global well-posedness for small data can be achieved via Strichartz estimates for the kinetic transport equation. Another new development in the thesis is connected to the question of the global regularity of the Dirac-Klein-Gordon system in space dimensions above one for large initial data. That question was instigated in the 1970’s by Chadam and Glassey [12, 13, 22] and although a great number of mathematicians have made contributions in the past 30 years, we, together with the independent recent preprint by Gr¨unrock and Pecher [24], present the first global result for large data. In particular, we prove that in two space dimensions the system has spherically symmetric solutions for all time if the initial data is spherically symmetric and lies in a certain regularity class. Our result is achieved via new inhomogeneous Strichartz estimates for spherically symmetric functions that we prove in the abstract setting and in particular for the wave equation. We make a number of other lesser improvements and generalizations in relation to the Strichartz estimates that shall be presented in the main body of this text.
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Savostianov, Anton. "Strichartz estimates and smooth attractors of dissipative hyperbolic equations." Thesis, University of Surrey, 2015. http://epubs.surrey.ac.uk/808756/.

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In this thesis we prove attractor existence and its smoothness for several classes of damped wave equations with critical nonlinearity. The term "critical" refers to the fact that behaviour of the solutions is determined not only by the energy but also by some more subtle space-time norms which are known as Strichartz norms. One of the main achievements of the work is the construction of the global attractor to the so called weakly damped wave equation with nonlinearity that admits fifth order polynomial growth. This problem was open from the first part of the 90's and its solution required combination of tools from various branches of mathematics. The ideas that we have developed we apply to several classes of wave equation with non-local damping. In this case the amount of energy dissipation that occurs in a fixed bunch of space depends on the solution in the whole region where the problem is considered. Though this model may seem to be more complicated at first sight, in fact, in this case solutions of the corresponding problem possess better regularizing properties. Finally we would like to remark that the developed ideas have general nature and thus open new opportunities for further investigations. In particular, the newly discovered techniques and ideas have already been successfully implemented for the construction of the global attractor in problems of phase separation.
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Blair, Matthew D. "Strichartz estimates for wave equations with coefficients of Sobolev regularity /." Thesis, Connect to this title online; UW restricted, 2005. http://hdl.handle.net/1773/5745.

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Meas, Len. "Estimations de dispersion et de Strichartz dans un domaine cylindrique convexe." Thesis, Université Côte d'Azur (ComUE), 2017. http://www.theses.fr/2017AZUR4038/document.

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Dans ce travail, nous allons établir des estimations de dispersion et des applications aux inégalités de Strichartz pour les solutions de l’équation des ondes dans un domaine cylindrique convexe Ω ⊂ R³ à bord C∞, ∂Ω ≠ ∅. Les estimations de dispersion sont classiquement utilisées pour prouver les estimations de Strichartz. Dans un domaine Ω général, des estimations de Strichartz ont été démontrées par Blair, Smith, Sogge [6,7]. Des estimations optimales ont été prouvées dans [29] lorsque Ω est strictement convexe. Le cas des domaines cylindriques que nous considérons ici généralise les resultats de [29] dans le cas où la courbure positive dépend de l'angle d'incidence et s'annule dans certaines directions
In this work, we establish local in time dispersive estimates and its application to Strichartz estimates for solutions of the model case Dirichlet wave equation inside cylindrical convex domains Ω ⊂ R³ with smooth boundary ∂Ω ≠ ∅. Let us recall that dispersive estimates are key ingredients to prove Strichartz estimates. Strichartz estimates for waves inside an arbitrary domain Ω have been proved by Blair, Smith, Sogge [6,7]. Optimal estimates in strictly convex domains have been obtained in [29]. Our case of cylindrical domains is an extension of the result of [29] in the case where the nonnegative curvature radius depends on the incident angle and vanishes in some directions
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Bolleyer, Andreas [Verfasser], and L. [Akademischer Betreuer] Weis. "Spectrally Localized Strichartz Estimates and Nonlinear Schrödinger Equations / Andreas Bolleyer. Betreuer: L. Weis." Karlsruhe : KIT-Bibliothek, 2015. http://d-nb.info/1071894269/34.

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Metcalfe, Jason L. "Global Strichartz estimates for solutions of the wave equation exterior to a convex obstacle." Available to US Hopkins community, 2003. http://wwwlib.umi.com/dissertations/dlnow/308072.

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Negro, Giuseppe. "Sharp estimates for linear and nonlinear wave equations via the Penrose transform." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCD071.

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Nous appliquons la transformée de Penrose, qui est un outil basique de la physique relativiste, à des estimations optimales pour les équations des ondes linéaire et non linéaire. Nous infirmons une conjecture de Foschi concernant les points extrémaux de l’inégalité de Strichartz à données dans l’espace de Sobolev Ḣ½ x Ḣ⁻½ (Rᵈ) où d ⩾2 est pair. En revanche, nous donnons des indications appuyant cette conjecture en dimension impaire, ainsi qu’une version raffinée de son inégalité optimale sur R¹⁺³, en ajoutant un terme proportionnel à la distance des données initiales de l’ensemble des points extrémaux. À l’aide de ce résultat, nous obtenons une formule asymptotique pour la norme de Strichartz des solutions petites de l’équation des ondes cubique dans l’espace-temps de Minkowski. Le coefficient principal est donné par la constante optimale de Foschi. Nous calculons le terme suivant, qui change de signe et de valeur absolue selon que la non-linéarité est focalisante ou défocalisante
We apply the Penrose transform, which is a basic tool of relativistic physics, to the study of sharp estimates for linear and nonlinear wave equations. We disprove a conjecture of Foschi, regarding extremizers for the Strichartz inequality with data in the Sobolev space Ḣ½ x Ḣ⁻½ (Rᵈ), for even d ⩾2. On the other hand, we provide evidence to support the conjecture in odd dimensions and refine his sharp inequality in R¹⁺³, adding a term proportional to the distance of the initial data from the set of extremizers. Using this, we provide an asymptotic formula for the Strichartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi’s sharp constant. We calculate the constant in the second term, whose absolute value and sign changes depending on whether the equation is focusing or defocusing
Aplicamos la transformada de Penrose, una herramienta básica de la fı́sica relativista, a unas estimaciones óptimas para ecuaciones de ondas lineales y no lineales. Invalidamos una conjetura de Foschi, sobre extremizadores para la estimación de Strichartz con datos en el espaciode Sobolev Ḣ½ x Ḣ⁻½ (Rᵈ), para d ⩾2 par. Por otro lado, vamos a dar indicios en favor de su conjetura en dimension impar, ası́ como una versión refinada de su desigualdad óptimaen R¹⁺³, añadiendo un término proporcional a la distancia de los datos iniciales del conjuntode puntos extremales. Utilizando este resultado, conseguimos una fórmula asintótica para la norma de Strichartz de soluciones pequeñas de la ecuación de ondas cúbica en el espacio-tiempo de Minkowski. El coeficiente principal coincide con la constante óptima de Foschi. Calculamos explı́citamente el coeficiente del otro término, cuyo módulo y signo cambian dependiendo de siestamos en el caso focusing o defocusing
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Chen, I.-Kun. "Spherical averaged endpoint Strichartz estimates for the two-dimensional Schrodinger equations with inverse square potential." College Park, Md.: University of Maryland, 2009. http://hdl.handle.net/1903/9473.

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Thesis (Ph.D.) -- University of Maryland, College Park, 2009.
Thesis research directed by: Dept. of Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Abdelkaled, Houda. "Caractère bien posé probabiliste pour une équation non linéaire faiblement dispersive." Thesis, CY Cergy Paris Université, 2020. http://www.theses.fr/2020CYUN1075.

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Nous nous proposons dans cette thèse d’étudier la propagation d’ondes non-linéairesdans le régime haute fréquence par des méthodes provenant de la théorie des probabilitéset de la théorie des équations aux dérivées partielles. On considère l’équation d’onde fractionnaire cubique, posée sur un domaine borné de l’espace euclidien, avec des conditionsau bord périodiques. On montrera pour commencer, sur quels espaces ce problème estbien-posé au sens d’Hadamard à l’aide de méthodes de point fixe. Dans un deuxièmetemps, on va démontrer des résultats d’instabilité à haute fréquence qui montrent leslimites des méthodes standards. Pour finir, on envisagera de construire des mesures deprobabilité sur l’espace des données initiales telles que dans le contexte des résultatsd’instabilité, une forme de caractère bien-posé persiste, presque surement
We propose in this thesis to study the propagation of non-linear wavesin the high frequency regime by methods from probability theoryand the theory of partial differential equations. We consider the cubic fractional wave equation, posed on a bounded domain of Euclidean space, with conditionsat the edge periodic. We will show to begin with, on which spaces this problem iswell-posed in Hadamard’s sense using fixed point methods. Then, we're going to proof high frequency instability results that shows thelimit of standard methods. Finally, we will consider building probabilistic measures on the space of the initial data such as in the context of the instability results, a well-posedness form persists, almost surely
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Books on the topic "Strichartz estimates"

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Robbiano, Luc, and Claude Zuily. Strichartz Estimates for Schrodinger Equations With Variable Coefficients. Societe Mathematique De France, 2005.

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Dispersive and Strichartz Estimates for Hyperbolic Equations with Constant Coefficients. Mathematical Society of Japan, 2010.

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Dispersive and Strichartz Estimates for Hyperbolic Equations with Constant Coefficients. Tokyo, Japan: The Mathematical Society of Japan, 2010. http://dx.doi.org/10.2969/msjmemoirs/022010000.

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Book chapters on the topic "Strichartz estimates"

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Koch, Herbert, Daniel Tataru, and Monica Vişan. "Dispersive and Strichartz estimates." In Oberwolfach Seminars, 227–38. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0736-4_16.

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Lerner, Nicolas. "Carleman Estimates via Brenner’s Theorem and Strichartz Estimates." In Grundlehren der mathematischen Wissenschaften, 355–79. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-15993-1_9.

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Koch, Herbert, Daniel Tataru, and Monica Vişan. "Long-time Strichartz estimates and applications." In Oberwolfach Seminars, 281–89. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0736-4_23.

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Stefanov, Atanas. "Decay and Strichartz Estimates for DNLS." In Springer Tracts in Modern Physics, 401–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-89199-4_22.

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Faminskii, Andrei V. "On Strichartz Estimates in an Abstract Form." In Trends in Mathematics, 473–80. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-48812-7_60.

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Bahouri, Hajer, Jean-Yves Chemin, and Raphaël Danchin. "Strichartz Estimates and Applications to Semilinear Dispersive Equations." In Grundlehren der mathematischen Wissenschaften, 335–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-16830-7_8.

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Schippa, Robert. "On Strichartz Estimates from ℓ 2-Decoupling and Applications." In Trends in Mathematics, 279–89. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-47174-3_17.

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Bez, Neal, Chris Jeavons, and Nikolaos Pattakos. "Sharp Sobolev–Strichartz Estimates for the Free Schrödinger Propagator." In Trends in Mathematics, 281–88. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-12577-0_33.

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Koch, Herbert, Daniel Tataru, and Monica Vişan. "Strichartz estimates and small data for the nonlinear Schrödinger equation." In Oberwolfach Seminars, 23–39. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0736-4_3.

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Bez, Neal, Chris Jeavons, Tohru Ozawa, and Hiroki Saito. "A Conjecture Regarding Optimal Strichartz Estimates for the Wave Equation." In Trends in Mathematics, 293–99. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-48812-7_37.

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Conference papers on the topic "Strichartz estimates"

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Nikolova, Elena, Mirko Tarulli, and George Venkov. "Extended Strichartz estimates for the heat equation with a Strichartz type potential." In THERMOPHYSICAL BASIS OF ENERGY TECHNOLOGIES (TBET 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0042670.

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Nikolova, Elena, Mirko Tarulli, and George Venkov. "On the extended Strichartz estimates for the nonlinear heat equation." In PROCEEDINGS OF THE 45TH INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’19). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5133504.

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