Almost global existence of small solutions to quadratic nonlinear Schrödinger equations in three space dimensions

DOI10.1007/BF02572354zbMath0824.35026MaRDI QIDQ1895774

Nakao Hayashi, Jean Ginibre

Publication date: 29 August 1995

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174762

zbMATH Keywords

quadratic nonlinear Schrödinger equationssmall almost global solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) NLS equations (nonlinear Schrödinger equations) (35Q55) Initial value problems for nonlinear higher-order PDEs (35G25)

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Global solution for the \(3D\) quadratic Schrödinger equation of \(Q(u,\bar{u}\)) type ⋮ Space-time resonances ⋮ From the Gross-Pitaevskii equation to the Euler Korteweg system, existence of global strong solutions with small irrotational initial data ⋮ Global solutions for 2D quadratic Schrödinger equations ⋮ Remark on the global existence and large time asymptotics of solutions for the quadratic NLS ⋮ Global existence of small analytic solutions to schrodinger equations with quadratic nonlinearity ⋮ Global existence of small solutions to nonlinear Schrödinger equations ⋮ Quadratic derivative nonlinear Schrödinger equations in two space dimensions ⋮ Some non-existence results for the semilinear Schrödinger equation without gauge invariance ⋮ Small data blow-up of \(L^2\) or \(H^1\)-solution for the semilinear Schrödinger equation without gauge invariance

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