Well-posedness for a generalized derivative nonlinear Schrödinger equation

Masayuki Hayashi, Tohru Ozawa

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We study the Cauchy problem for a generalized derivative nonlinear Schrödinger 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
Externally publishedYes

Fingerprint

Generalized Derivatives
Sobolev spaces
Local Well-posedness
Nonlinear equations
Well-posedness
Global Existence
Sobolev Spaces
Dirichlet Boundary Conditions
Compactness
Existence of Solutions
Cauchy Problem
Nonlinear Equations
Approximate Solution
Boundary conditions
Derivatives
Energy

Keywords

  • Derivative nonlinear Schrödinger equation
  • Yosida regularization

ASJC Scopus subject areas

  • Analysis

Cite this

Well-posedness for a generalized derivative nonlinear Schrödinger equation. / Hayashi, Masayuki; Ozawa, Tohru.

In: Journal of Differential Equations, Vol. 261, No. 10, 15.11.2016, p. 5424-5445.

Research output: Contribution to journalArticle

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