Global existence for a coupled wave system related to the Strauss\n conjecture

2017/01/19 by Jason Metcalfe, Metcalfe, Jason, David J. Spencer +2
Engineering · Mathematics · Physics and Astronomy · #35L15 #35L70 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1701.05642

openalex publication_date 2017/01/19 · openalex created_date 2022/12/11 · openalex updated_date 2026/07/28

Abstract

A coupled system of semilinear wave equations is considered, and a small data\nglobal existence result related to the Strauss conjecture is proved. Previous\nresults have shown that one of the powers may be reduced below the critical\npower for the Strauss conjecture provided the other power sufficiently exceeds\nsuch. The stability of such results under asymptotically flat perturbations of\nthe space-time where an integrated local energy decay estimate is available is\nestablished.\n

Citations

• Errata for ``Global existence and scattering for the nonlinear Schrodinger equation on Schwarzschild manifolds'', ``Semilinear wave equations on the Schwarzschild manifold I: Local Decay Estimates'', and ``The wave equation on the Schwarzschild metric II: Local Decay for the spin 2 Regge Wheeler equation''

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