Well-posedness for a generalized derivative nonlinear Schrï¿½dinger equation

Masayuki Hayashi; Tohru Ozawa

doi:10.1016/j.jde.2016.08.018

Well-posedness for a generalized derivative nonlinear Schrï¿½dinger equation

Masayuki Hayashi^*, Tohru Ozawa

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

32 Citations (Scopus)

Abstract

We study the Cauchy problem for a generalized derivative nonlinear Schrï¿½dinger 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 language	English
Pages (from-to)	5424-5445
Number of pages	22
Journal	Journal of Differential Equations
Volume	261
Issue number	10
DOIs	https://doi.org/10.1016/j.jde.2016.08.018
Publication status	Published - 2016 Nov 15
Externally published	Yes

Keywords

Derivative nonlinear Schrï¿½dinger equation
Yosida regularization

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2016.08.018

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abstract = "We study the Cauchy problem for a generalized derivative nonlinear Schr{\"i}¿½dinger 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.",

keywords = "Derivative nonlinear Schr{\"i}¿½dinger equation, Yosida regularization",

author = "Masayuki Hayashi and Tohru Ozawa",

note = "Publisher Copyright: {\"i}¿½ 2016 Elsevier Inc.",

year = "2016",

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doi = "10.1016/j.jde.2016.08.018",

language = "English",

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AU - Hayashi, Masayuki

AU - Ozawa, Tohru

N1 - Publisher Copyright: ï¿½ 2016 Elsevier Inc.

PY - 2016/11/15

Y1 - 2016/11/15

N2 - We study the Cauchy problem for a generalized derivative nonlinear Schrï¿½dinger 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.

AB - We study the Cauchy problem for a generalized derivative nonlinear Schrï¿½dinger 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.

KW - Derivative nonlinear Schrï¿½dinger equation

KW - Yosida regularization

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DO - 10.1016/j.jde.2016.08.018

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JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 10

ER -

Well-posedness for a generalized derivative nonlinear Schrï¿½dinger equation

Abstract

Keywords

ASJC Scopus subject areas

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