Hokkaido Mathematical Journal

Nakanishi Kenji,

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

Hokkaido Mathematical Journal, 37 (2008) pp.749-771

Fulltext

PDF

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.

MSC(Primary)35L70
MSC(Secondary)35Q55, 35B40, 35B25
Uncontrolled Keywordsnonlinear Klein-Gordon equation, nonlinear Schrödinger equation, wellposedness, nonrelativistic limit.