On the global wellposedness for the nonlinear Schrödinger equations with \(L^{p}\)-large initial data

DOI10.1007/S00030-011-0097-2zbMath1219.35281OpenAlexW2003285297MaRDI QIDQ543482

Ryosuke Hyakuna, Masayoshi Tsutsumi

Publication date: 17 June 2011

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-011-0097-2

zbMATH Keywords

Cauchy problemglobal solutionnonlinear Schrödinger equationlarge inital 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)

Related Items (4)

Analytic smoothing effect for the nonlinear Schrödinger equations without square integrability ⋮ Local and global existence in L^p for the inhomogeneous nonlinear Schrödinger equation ⋮ Global solutions to the Hartree equation for large L^{p}-initial data ⋮ Local and global well-posedness, and \(L^{p^\prime}\)-decay estimates for 1D nonlinear Schrödinger equations with Cauchy data in \(L^p\)

Cites Work

• On the global well-posedness for the nonlinear Schrödinger equations with large initial data of infinite \(L^2\) norm
• Global wellposedness for 1D nonlinear Schrödinger equation for data with an infinite \(L^2\) norm
• A priori bounds and weak solutions for the nonlinear Schrödinger equation in Sobolev spaces of negative order
• On L(p,q) spaces
• Asymptotically-Free Solutions for the Short-Range Nonlinear Schrödinger Equation
• A NOTE ON THE NONLINEAR SCHRÖDINGER EQUATION IN WEAK L^pSPACES
• A Priori Bounds for the 1D Cubic NLS in Negative Sobolev Spaces
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