Stability of a class of semilinear waves in $2+1$ dimension under null condition

Abstract

We will show that in $\RR^{2+1}$ semilinear wave equations of the form $-\Box u = u Q(\del u; \del u)$ possess global-in-time solutions if the null condition on $Q(\del u; \del u)$ is assumed. As a consequence, we also provide a new proof, after \cite{Wong}, on the small data global solutions to the wave map equation in $\RR^{2+1}$ and no compactness assumptions on the initial data are needed.

14 pages, corrected typos, and added more information about the financial support

References in corpus (2)

• Global solutions of nonlinear wave-Klein-Gordon system in two spatial dimensions: weak coupling case
• Small data global existence and decay for two dimensional wave maps

Cited by in corpus (1)

• Global solution to the wave and Klein-Gordon system under null condition in dimension two