On well-posedness for nonlinear Schrödinger equations with power nonlinearity in fractional order Sobolev spaces

DOI10.1016/J.JMAA.2012.04.079zbMath1246.35190OpenAlexW1991881476MaRDI QIDQ441948

Takeshi Wada, Harunori Uchizono

Publication date: 8 August 2012

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.04.079

zbMATH Keywords

well-posednessnonlinear Schrödinger equationsfractional order Sobolev spaces

Mathematics Subject Classification ID

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) Besov spaces and (Q_p)-spaces (30H25)

Related Items (5)

On local well-posedness for \(H^s\)-critical nonlinear Schrödinger equations ⋮ Strichartz type estimates in mixed Besov spaces with application to critical nonlinear Schrödinger equations ⋮ Modified Strichartz estimates with an application to the critical nonlinear Schrödinger equation ⋮ A remark on local well-posedness for nonlinear Schrödinger equations with power nonlinearity -- an alternative approach ⋮ NON-REGULARITY IN HÖLDER AND SOBOLEV SPACES OF SOLUTIONS TO THE SEMILINEAR HEAT AND SCHRÖDINGER EQUATIONS

Cites Work

• Unnamed Item
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• Continuous dependence for NLS in fractional order spaces
• The global Cauchy problem for the nonlinear Schrödinger equation revisited
• Existence of solutions for Schrödinger evolution equations
• Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
• On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case
• On Besov spaces and Sobolev spaces of generalized functions defined on a general region
• On nonlinear Schrödinger equations. II: \(H^ S\)-solutions and unconditional well-posedness
• The cauchy problem for the critical nonlinear Schrödinger equation in Hs
• Global strong solutions for nonlinear Schrödinger equations
• Operator-Valued Fourier Multipliers, Vector - Valued Besov Spaces, and Applications
• Introduction to nonlinear dispersive equations

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