Well and ill-posedness issues for energy supercritical waves

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Ibrahim, Slim
Majdoub, Mohamed
Masmoudi, Nader
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Abstract
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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.
Comment: Submitted
Keywords
Mathematics - Analysis of PDEs, Mathematics - Classical Analysis and ODEs, 35L05, 49K40, 65F22, 34-XX, 34Cxx, 34C25
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