Well and ill-posedness issues for energy supercritical waves

Details Well and ill-posedness issues for energy supercritical waves Well and ill-posedness issues for energy supercritical waves

2009-06-17

arxiv.org/abs/0906.3092v1

Mathematics

Analysis of PDEs

Submitted

Scientific paper

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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