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arXiv · 0906.3092

Well and ill-posedness issues for energy supercritical waves

Slim Ibrahim·Mohamed Majdoub·Nader Masmoudi
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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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Slim Ibrahim, Mohamed Majdoub, Nader Masmoudi. 2009-06-17. Well and ill-posedness issues for energy supercritical waves. https://arxiv.org/abs/0906.3092

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