Random data Cauchy theory for supercritical wave equations II : A global existence result

Details Random data Cauchy theory for supercritical wave equations II : A global existence result Random data Cauchy theory for supercritical wave equations II : A global existence result

2007-07-10

arxiv.org/abs/0707.1448v1

Mathematics

Analysis of PDEs

Scientific paper

10.1007/s00222-008-0123-0

We prove that the subquartic wave equation on the three dimensional ball $\Theta$, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in $\cap_{s<1/2} H^s(\Theta)$. We obtain this result as a consequence of a general random data Cauchy theory for supercritical wave equations developed in our previous work \cite{BT2} and invariant measure considerations which allow us to obtain also precise large time dynamical informations on our solutions.

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