On Global existence for nonlinear wave equations outside of convex obstacles

1999/12/26 by Marcus Keel, Hart F. Smith, Hart Smith +4 · 1 citation
Engineering · Mathematics · #35L70 #42B99 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #math.CA #msc:35L70 #msc:42B99

paper · pdf · doi:10.48550/arxiv.math/9912201

To appear in American Journal of Mathematics

arxiv created 1999/12/26 · openalex publication_date 1999/12/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove global existence for semilinear hyperbolic equations that satisfy the null condition of Christodoulou and Klainerman in the exterior of convex domains. We use a combination of the conformal method of Christodoulou and the direct method of Klainerman.

Citations

• Space‐time estimates for null forms and the local existence theorem

Cited by

• Global smooth solutions of 2-D quadratically quasilinear wave equations with null conditions in exterior domains, II

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