Time decay of solutions to the Cauchy problem for time-dependent Schrödinger-Hartree equations

DOI10.1007/BF01212423zbMath0648.35078MaRDI QIDQ1105127

Nakao Hayashi, Tohru Ozawa

Publication date: 1987

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

estimatesunique global solutiontime-dependent Schrödinger-Hartree equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Stability in context of PDEs (35B35) Nonlinear higher-order PDEs (35G20) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

LONG RANGE SCATTERING AND MODIFIED WAVE OPERATORS FOR SOME HARTREE TYPE EQUATIONS I, Unnamed Item, Time decay for some Schrödinger equations, Energy criteria of global existence for a class of Hartree equations with Coulomb potential, On the Cauchy problem for the Hartree type semilinear Schrödinger equation in the de Sitter spacetime, Smoothing effects and dispersion of singularities for the Schrödinger evolution group, Space-time behavior of propagators for Schrödinger evolution equations with Stark effect, On nonlinear Schrödinger equations with attractive inverse-power potentials, Nonlinear scattering with nonlocal interaction, MODIFIED SCATTERING FOR BIPOLAR NONLINEAR SCHRÖDINGER–POISSON EQUATIONS, A remark on some papers by N. Hayashi and T. Ozawa, On nonlinear Schrödinger equations with repulsive inverse-power potentials, On the time dependence of the rate of convergence towards Hartree dynamics for interacting bosons, Smoothing effect for some Schrödinger equations, A nonlinear Schrödinger equation with Coulomb potential

Cites Work

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• Weighted Sobolev spaces and rapidly decreasing solutions of some nonlinear dispersive wave equations
• Asymptotic behavior of solutions to certain nonlinear Schrödinger-Hartree equations
• On a class of nonlinear Schrödinger equations. II. Scattering theory, general case
• Asymptotic behavior of solutions to time-dependent Hartree equations
• Global existence of solutions to the Cauchy problem for time-dependent Hartree equations