Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions

Details Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions Asymptotic pointwise behavior for systems of semilinear wave equations in three space dimensions

2011-01-19

arxiv.org/abs/1101.3657v1

Mathematics

Analysis of PDEs

51 pages

Scientific paper

In connection with the weak null condition, Alinhac introduced a sufficient condition for global existence of small amplitude solutions to systems of semilinear wave equations in three space dimensions. We introduce a slightly weaker sufficient condition for the small data global existence, and we investigate the asymptotic pointwise behavior of global solutions for systems satisfying this condition. As an application, the asymptotic behavior of global solutions under the Alinhac condition is also derived.

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