Well and ill-posedness issues for energy supercritical waves

2009/06/17 by Slim Ibrahim, Ibrahim, Slim, Mohamed Majdoub +3
Mathematics · #34-XX #34C25 #34Cxx #35L05 #49K40 #65F22 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AP #math.CA #msc:34-XX #msc:34C25 #msc:34Cxx #msc:35L05 #msc:49K40 #msc:65F22

paper · pdf · doi:10.48550/arxiv.0906.3092

Submitted

arxiv created 2009/06/17 · arxiv updated 2009/12/01

Abstract

We investigate the initial value problem for some energy supercritical semilinear wave equations. We establish local existence in suitable spaces with continuous flow. We also obtain some ill-posedness/weak ill-posedness results. The proof uses the finite speed of propagation and a quantitative study of the associated ODE. It does not require any scaling invariance of the equation.

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