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arXiv · 0707.1448

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

N. Burq·N. Tzvetkov
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Abstract

We prove that the subquartic wave equation on the three dimensional ball $Θ$, with Dirichlet boundary conditions admits global strong solutions for a large set of random supercritical initial data in $\cap_{s<1/2} H^s(Θ)$. 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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N. Burq, N. Tzvetkov. 2007-07-10. Random data Cauchy theory for supercritical wave equations II : A global existence result. https://doi.org/10.1007/s00222-008-0123-0

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