Hokkaido Mathematical Journal

Transfer of global wellposedness from nonlinear Klein-Gordon equation to nonlinear Schrödinger equation

Kenji NAKANISHI

Full-text: Open access

Abstract

We discuss relations between the nonlinear Klein-Gordon equation and the nonlinear Schrödinger equation in view of the global wellposedness in the energy space and L^2. In some critical cases, we show that the global wellposedness for the former equation with some uniform bounds implies that for the latter.

Article information

Source
Hokkaido Math. J., Volume 37, Number 4 (2008), 749-771.

Dates
First available in Project Euclid: 31 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1249046367

Digital Object Identifier
doi:10.14492/hokmj/1249046367

Mathematical Reviews number (MathSciNet)
MR2474174

Zentralblatt MATH identifier
1184.35215

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35B40: Asymptotic behavior of solutions 35B25: Singular perturbations

Keywords
nonlinear Klein-Gordon equation nonlinear Schrödinger equation wellposedness nonrelativistic limit

Citation

NAKANISHI, Kenji. Transfer of global wellposedness from nonlinear Klein-Gordon equation to nonlinear Schrödinger equation. Hokkaido Math. J. 37 (2008), no. 4, 749--771. doi:10.14492/hokmj/1249046367. https://projecteuclid.org/euclid.hokmj/1249046367


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