Strichartz estimates for Schrödinger equations with variable coefficients

Luc Robbiano, Claude Zuily

Type: Article

Publication Date: 2005-01-01

Citations: 38

DOI: https://doi.org/10.24033/msmf.414

Abstract

On demontre les inegalites de Strichartz (locales en temps) pour l'ensemble des indices donnes par l'invariance d'echelle (sauf le point final) pour des perturbations asymptotiquement plates et non captantes du laplacien usuel de R n , n ≥ 2. Le point principal de la preuve, a savoir l'estimation de dispersion, est obtenu en construisant une parametrixe. L'outil principal de cette construction est la theorie de la transformation de FBI construite par Sjostrand.

Locations

Mémoires de la Société mathématique de France - View
arXiv (Cornell University) - View
French digital mathematics library (Numdam) - View - PDF
HAL (Le Centre pour la Communication Scientifique Directe) - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Dispersion et inégalités de Strichartz pour l'équation de Schrödinger 1D à coefficients variables	2005	Delphine Salort
+	Strichartz estimates for Schrodinger equations with variable coefficients(Spectral and Scattering Theory and Related Topics)	2006	Luc Robbiano Claude Zuily
+	Estimées de Strichartz pour l’équation de Schrödinger à coefficients variables	2004	Luc Robbiano Claude Zuily
+	Strichartz Estimates for Schrödinger Equations with Variable Coefficients	2005	Luc Robbiano Claude Zuily
+	Estimations de Strichartz généralisées sur le groupe de Heisenberg	1998	Hajer Bahouri Patrick Gérard Chao-Jiang Xu
+	Equations dispersives et problèmes aux limites	2009	Danela Oana Ivanovici
+	Strichartz Estimates for Schrödinger Equations with Non-degenerate Coefficients*	2007	Miao Yu
+ PDF Chat	Strichartz estimates for Schrödinger-Laguerre operators	2014	Salem Ben Saïd
+ PDF Chat	The Schrödinger equation on a compact manifold : Strichartz estimates and applications	2001	Nicolas Burq Patrick Gérard Nikolay Tzvetkov
+	Strichartz Estimates for the Schroedinger equation	2010	Elena Cordero Davide Zucco
+	Strichartz type estimates for solutions to the Schrödinger equation	2024	Jie Chen
+	Strichartz Estimates for Schroedinger Equations with Non-degenerate Coefficients	2007	Yu Miao
+ PDF Chat	Sharp estimates for linear and nonlinear wave equations via the Penrose transform	2018	Giuseppe Negro
+ PDF Chat	Sharp Strichartz estimates for the Schrödinger equation on the sphere	2021	Duván Cardona Liliana Esquivel
+	Etude mathématique de quelques modèles d'équations d'ondes sur des variétés équipées de métrique singulière	2008	Zakaria Hachemaoui
+ PDF Chat	Strichartz estimates and local smoothing estimates for asymptotically flat Schrödinger equations	2008	Jeremy L. Marzuola Jason Metcalfe Daniel Tataru
+	Local smoothing property and Strichartz inequality for Schrodinger equations with potentials superquadratic at infinity (Spectral and Scattering Theory and Related Topics)	2002	Kenji Yajima Guoping Zhang
+	Problèmes d'existence en temps grand pour des équations de Kein-Gordon non-linéaires	2006	Alin Laurentiu Benoaga
+	Effets régularisants et existence locale pour les équations non-linéaires de Schrödinger et des plaques à coefficients variables	2001	Laurent T'Joen
+	Effets dispersifs et asymptotique en temps long d'équations d'ondes dans des domaines extérieurs	2018	David Lafontaine

Works That Cite This (36)

Action	Title	Year	Authors
+	Long-term regularity of 3D gravity water waves	2019	Fan Zheng
+ PDF Chat	Semiclassical singularities propagation property for Schrödinger equations	2009	Shu Nakamura
+	Endpoint Strichartz estimates for the magnetic Schrödinger equation	2010	Piero DʼAncona Luca Fanelli Luis Vega Nicola Visciglia
+	On global Strichartz estimates for non-trapping metrics	2008	Jean‐Marc Bouclet Nikolay Tzvetkov
+ PDF Chat	Time Decay of Scaling Invariant Electromagnetic Schrödinger Equations on the Plane	2015	Luca Fanelli Veronica Felli Marco A. Fontelos Ana Primo
+ PDF Chat	Global existence for defocusing cubic NLS and Gross–Pitaevskii equations in three dimensional exterior domains	2008	Ramona Anton
+ PDF Chat	Dispersion and Strichartz estimates for the Liouville equation	2006	Delphine Salort
+ PDF Chat	Weighted Strichartz estimates for radial Schrödinger equation on noncompact manifolds	2007	Valeria Banica Thomas Duyckaerts
+	Global in time Strichartz inequalities on asymptotically flat manifolds with temperate trapping	2016	Jean‐Marc Bouclet Haruya Mizutani
+	Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem	2007	Patrick Gérard

Works Cited by This (6)

Action	Title	Year	Authors
+	The analysis of linear partial differential operators	1990	Lars Hörmander
+ PDF Chat	Sharp Strichartz estimates on nontrapping asymptotically conic manifolds	2006	Andrew Hassell Terence Tao Jared Wunsch
+ PDF Chat	STRICHARTZ ESTIMATES FOR A SCHRÖDINGER OPERATOR WITH NONSMOOTH COEFFICIENTS	2002	Gigliola Staffilani Daniel Tataru
+ PDF Chat	Smoothing properties and retarded estimates for some dispersive evolution equations	1992	J. Ginibre G. Velo
+	Fourier integral operators with complex-valued phase functions	1975	Anders Melin Johannes Sjöstrand
+ PDF Chat	Analytic theory for the quadratic scattering wave front set and application to the Schrödinger equation	2018	Luc Robbiano Claude Zuily