EFFETS RÉGULARISANTS ET EXISTENCE LOCALE POUR L'ÉQUATION DE SCHRÖDINGER NON-LINÉAIRE À COEFFICIENTS VARIABLES

DOI10.1081/PDE-120002865zbMath1005.35089OpenAlexW3150136687MaRDI QIDQ4547608

Laurent Tjoën

Publication date: 19 February 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120002865

zbMATH Keywords

a priori estimatesnonlinear Schrödinger equationpseudodifferential operatorexistence of a unique solutiontrapped bicharacteristics

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Pseudodifferential operators as generalizations of partial differential operators (35S05) NLS equations (nonlinear Schrödinger equations) (35Q55) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items

Gain of analyticity for semilinear Schrödinger equations ⋮ Blow-up solutions of inhomogeneous nonlinear Schrödinger equations ⋮ Effective limiting absorption principles, and applications ⋮ Inhomogeneous critical nonlinear Schrödinger equations with a harmonic potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Regularity of solutions to the Schrödinger equation
• On some Schrödinger type equations
• Local smoothing and convergence properties of Schrödinger type equations
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
• Regularity in time of solutions to nonlinear Schrödinger equations
• On singularities of solutions of the Schrödinger equation for a free particle
• Dispersive smoothing for Schrödinger equations
• Smoothing effects of Schrödinger evolution groups on Riemannian manifolds
• Gain of regularity for semilinear Schrödinger equations
• Propagation of singularities and growth for Schrödinger operators
• Microlocal analytic smoothing effect for the Schrödinger equation
• The initial value problem for cubic semilinear Schrödinger equations
• Global strong solutions for nonlinear Schrödinger equations
• Commutator estimates and the euler and navier-stokes equations
• On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Effets régularisants et existence locale pour l'équation de Schrödinger non linéaire à coefficients variables
• Effect régularisant microlocal analytique pour l'équation de Schrödinger le cas des données oscillantes
• Global, small amplitude solutions to nonlinear evolution equations
• Microlocal dispersive smoothing for the Schrödinger equation
• Global extstence of small solutions to semiliner schrödinger equations
• Remarks on the cauchy problem for schrödinger-type equations
• The Cauchy problem for Schrödinger type equations with variable coefficients