Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains

2004/09/20 by Jason Metcalfe, Makoto Nakamura, Metcalfe, Jason +3
Mathematics · #35L70 #42B99 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35L70 #msc:42B99

paper · pdf · doi:10.48550/arxiv.math/0409362

30 pages. To appear in Forum Math

arxiv created 2004/09/20 · arxiv updated 2009/12/01

Abstract

In this paper we prove global existence for certain multispeed Dirichlet-wave equations with quadratic nonlinearities outside of obstacles. We assume the natural null condition for systems of quasilinear wave equations with multiple speeds. The null condition only puts restrictions on the self-interactions of each wave family. We use the method of commuting vector fields and weighted space-time L² estimates.

Related

• Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition
• Global existence for nonlinear wave equations with multiple speeds
• Global existence for a system of multiple-speed wave equations violating the null condition
• The global existence theorem for quasi-linear wave equations with multiple speeds, II
• Almost global existence for quasilinear wave equations in three space dimensions