Well-posedness for a generalized derivative nonlinear Schr�dinger equation

Masayuki Hayashi, Tohru Ozawa

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

We study the Cauchy problem for a generalized derivative nonlinear Schr�dinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces H1 and H2. Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space H1.

Original languageEnglish
Pages (from-to)5424-5445
Number of pages22
JournalJournal of Differential Equations
Volume261
Issue number10
DOIs
Publication statusPublished - 2016 Nov 15

Keywords

  • Derivative nonlinear Schr�dinger equation
  • Yosida regularization

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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