Local well-posedness for the inhomogeneous nonlinear Schrödinger equation in \(H^s ( \mathbb{R}^n )\)

DOI10.1016/J.NONRWA.2020.103268zbMath1468.35183OpenAlexW3112887298MaRDI QIDQ2025423

JinMyong An, Jin-Myong Kim

Publication date: 14 May 2021

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2020.103268

zbMATH Keywords

Cauchy problemlocal well-posednessinhomogeneous nonlinear Schrödinger equationsubcritical

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Time-dependent Schrödinger equations and Dirac equations (35Q41) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (8)

The Cauchy problem for the critical inhomogeneous nonlinear Schrödinger equation in \(H^s(\mathbb{R}^n)\) ⋮ A note on the \(H^s\)-critical inhomogeneous nonlinear Schrödinger equation ⋮ Small data global well-posedness for the inhomogeneous biharmonic NLS in Sobolev spaces ⋮ Bilinear Strichartz's type estimates in Besov spaces with application to inhomogeneous nonlinear biharmonic Schrödinger equation ⋮ Small data global well-posedness and scattering for the inhomogeneous nonlinear Schrödinger equation in \(H^s (\mathbb{R}^n)\) ⋮ Continuous dependence of the Cauchy problem for the inhomogeneous nonlinear Schrödinger equation in \(H^s (\mathbb{R}^n)\) ⋮ Global existence and blow-up for the focusing inhomogeneous nonlinear Schrödinger equation with inverse-square potential ⋮ Local well-posedness for the inhomogeneous biharmonic nonlinear Schrödinger equation in Sobolev spaces

Cites Work

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• Global well-posedness and blow-up on the energy space for the inhomogeneous nonlinear Schrödinger equation
• Classification of minimal mass blow-up solutions for an \({L^{2}}\) critical inhomogeneous NLS
• Scattering for the radial 3D cubic focusing inhomogeneous nonlinear Schrödinger equation
• Scattering theory for the defocusing energy-supercritical nonlinear wave equation with a convolution
• Scattering above energy norm of solutions of a loglog energy-supercritical Schrödinger equation with radial data
• An inhomogeneous, \(L^2\)-critical, nonlinear Schrödinger equation
• Schrödinger equations with a spatially decaying nonlinearity: existence and stability of standing waves
• Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation
• Blowup of \(H^1\) solutions for a class of the focusing inhomogeneous nonlinear Schrödinger equation
• Nonlinear scattering theory for a class of wave equations in \(H^{s}\)
• Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation
• On well posedness for the inhomogeneous nonlinear Schrödinger equation
• Continuous dependence of Cauchy problem for nonlinear Schrödinger equation in \(H^s\)
• Classical Fourier Analysis
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
• Introduction to nonlinear dispersive equations

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