Global Well-Posedness and Scattering for Derivative Schrödinger Equation

DOI10.1080/03605302.2011.600798zbMath1229.35277arXiv0909.3611OpenAlexW1972311032MaRDI QIDQ3106543

Yu-Zhao Wang

Publication date: 28 December 2011

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.3611

zbMATH Keywords

scatteringBesov spacesglobal well-posednessderivative Schrödinger equationsnon-elliptic case

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Harmonic analysis and PDEs (42B37)

Related Items (2)

Small data well-posedness for derivative nonlinear Schrödinger equations ⋮ Optimal small data scattering for the generalized derivative nonlinear Schrödinger equations

Cites Work

• Global Schrödinger maps in dimensions \(d\geq 2\): small data in the critical Sobolev spaces
• The Cauchy problem for quasi-linear Schrödinger equations
• The general quasilinear ultrahyperbolic Schrödinger equation
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• Global well-posedness and scattering for the derivative nonlinear Schrödinger equation with small rough data
• Global existence of small solutions to nonlinear evolution equations
• Long-time behavior of solutions to nonlinear evolution equations
• Schrödinger flow of maps into symplectic manifolds
• Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations
• Global existence of small solutions to semilinear Schrödinger equations with gauge invariance
• Low-regularity Schrödinger maps. II: Global well-posedness in dimensions \(d \geq 3\)
• Global existence of small classical solutions to nonlinear Schrödinger equations
• The initial value problem for cubic semilinear Schrödinger equations
• Coherent structures in strongly interacting many-body systems. I. Derivation of dynamics
• Coherent structures in strongly interacting many-body systems. II. Classical solutions and quantum fluctuations
• Exact solutions of the multidimensional derivative nonlinear Schrodinger equation for many-body systems of criticality
• Endpoint Strichartz estimates
• Global, small amplitude solutions to nonlinear evolution equations

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