Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition

2004/09/20 by Jason Metcalfe, Makoto Nakamura, Metcalfe, Jason +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35L70 #msc:42B99

paper · pdf · doi:10.48550/arxiv.math/0409363

65 pages

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

Abstract

We prove global existence of solutions to multiple speed, Dirichlet-wave equations with quadratic nonlinearities satisfying the null condition in the exterior of compact obstacles. This extends the result of our previous paper by allowing general higher order terms. In the currect setting, these terms are much more difficult to handle than for the free wave equation, and we do so using an analog of a pointwise estimate due to Kubota and Yokoyama.

Citations

• On almost global existence for nonrelativistic wave equations in 3D
• Uniform decay estimates and the lorentz invariance of the classical wave equation

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• Global existence for Dirichlet-wave equations with quadratic nonlinearties in high dimensions
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• Global existence for semilinear wave equations exterior to nontrapping obstacles