The Cauchy problem for non-linear higher order Hartree type equation in modulation spaces

DOI10.1007/s00041-018-9629-zzbMath1420.35368OpenAlexW2809927866WikidataQ129649683 ScholiaQ129649683MaRDI QIDQ2003591

Ramesh Manna

Publication date: 9 July 2019

Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00041-018-9629-z

zbMATH Keywords

well-posednessmodulation spacesnon-linear Hartree equation

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Initial value problems for nonlinear higher-order PDEs (35G25) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (2)

Phase space analysis of the Hermite semigroup and applications to nonlinear global well-posedness ⋮ Global Cauchy problems for the Klein-Gordon, wave and fractional Schr\"odinger equations with Hartree nonlinearity on modulation spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Isometric decomposition operators, function spaces \(E_{p,q}^{\lambda}\) and applications to nonlinear evolution equations
• The global Cauchy problem for the NLS and NLKG with small rough data
• Fourier multipliers of classical modulation spaces
• Time-frequency analysis of Sjöstrand's class
• Unimodular Fourier multipliers for modulation spaces
• The Cauchy problem for nonlinear Schrödinger equations in modulation spaces
• The Cauchy problem for the Hartree type equation in modulation spaces
• Sparsity of Gabor representation of Schrödinger propagators
• Remarks on Fourier multipliers and applications to the wave equation
• Decay and scattering of solutions of a nonlinear Schrödinger equation
• On a class of non linear Schrödinger equations with non local interactions
• Continuity properties for modulation spaces, with applications to pseudo-differential calculus. I.
• Foundations of time-frequency analysis
• Phase space analysis of semilinear parabolic equations
• Stability of nonlinear Schrödinger equations on modulation spaces
• The dilation property of modulation spaces and their inclusion relation with Besov spaces
• Modulation spaces and non-linear Hartree type equations
• Remarks on nonlinear operations on modulation spaces
• Fourier Analysis and Nonlinear Partial Differential Equations
• Local well-posedness of nonlinear dispersive equations on modulation spaces
• Asymptotics for large time of solutions to the nonlinear Schrodinger and Hartree equations
• Global existence of solutions to the Cauchy problem for time-dependent Hartree equations
• Modulation Spaces and Nonlinear Evolution Equations
• On the Cauchy problem for the Hartree type equation in the Wiener algebra
• Solutions to nonlinear higher order Schrödinger equations with small initial data on modulation spaces

This page was built for publication: The Cauchy problem for non-linear higher order Hartree type equation in modulation spaces