On the global well-posedness for the nonlinear Schrödinger equations with large initial data of infinite $L^2$ norm

DOI10.1016/j.na.2010.10.003zbMath1206.35228OpenAlexW2003322565MaRDI QIDQ622402

Masayoshi Tsutsumi, Ryosuke Hyakuna, Takamasa Tanaka

Publication date: 31 January 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.10.003

zbMATH Keywords

Cauchy problem global solution nonlinear Schrödinger equations large initial data $L^p$-initial data

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Analytic smoothing effect for the nonlinear Schrödinger equations without square integrability ⋮ Local and global existence in L^p for the inhomogeneous nonlinear Schrödinger equation ⋮ On the global wellposedness for the nonlinear Schrödinger equations with $L^{p}$-large initial data ⋮ On the existence of global solutions of the one-dimensional cubic NLS for initial data in the modulation space $M_{p, q}(\mathbb{R})$ ⋮ Global solutions to the Hartree equation for large L^{p}-initial data ⋮ On the existence of global solutions of the Hartree equation for initial data in the modulation space $M^{p , q}(\mathbb{R})$ ⋮ On existence of global solutions of Schrödinger equations with subcritical nonlinearity for $̂L^{p}$-initial data

Cites Work

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On the global well-posedness for the nonlinear Schrödinger equations with large initial data of infinite \(L^2\) norm