Global existence of small classical solutions to nonlinear Schrödinger equations

Tohru Ozawa, Jian Zhai

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

We study the global Cauchy problem for nonlinear Schrödinger equations with cubic interactions of derivative type in space dimension n ≥ 3. The global existence of small classical solutions is proved in the case where every real part of the first derivatives of the interaction with respect to first derivatives of wavefunction is derived by a potential function of quadratic interaction. The proof depends on the energy estimate involving the quadratic potential and on the endpoint Strichartz estimates.

Original languageEnglish
Pages (from-to)303-311
Number of pages9
JournalAnnales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
Volume25
Issue number2
DOIs
Publication statusPublished - 2008 Mar
Externally publishedYes

Fingerprint

Classical Solution
Nonlinear equations
Global Existence
Nonlinear Equations
Derivatives
Derivative
Interaction
Strichartz Estimates
Energy Estimates
Potential Function
Wave functions
Cauchy Problem

Keywords

  • Nonlinear Schrödinger equations
  • Schrödinger maps

ASJC Scopus subject areas

  • Analysis

Cite this

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abstract = "We study the global Cauchy problem for nonlinear Schr{\"o}dinger equations with cubic interactions of derivative type in space dimension n ≥ 3. The global existence of small classical solutions is proved in the case where every real part of the first derivatives of the interaction with respect to first derivatives of wavefunction is derived by a potential function of quadratic interaction. The proof depends on the energy estimate involving the quadratic potential and on the endpoint Strichartz estimates.",
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AU - Zhai, Jian

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AB - We study the global Cauchy problem for nonlinear Schrödinger equations with cubic interactions of derivative type in space dimension n ≥ 3. The global existence of small classical solutions is proved in the case where every real part of the first derivatives of the interaction with respect to first derivatives of wavefunction is derived by a potential function of quadratic interaction. The proof depends on the energy estimate involving the quadratic potential and on the endpoint Strichartz estimates.

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KW - Schrödinger maps

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