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

2007/07/10 by N. Burq, N. Tzvetkov
Mathematics · #math.AP #msc:35Q55 #msc:35BXX #msc:37K05 #msc:37L50 #msc:81Q20

paper · pdf · doi:10.1007/s00222-008-0123-0

arxiv created 2007/07/10 · arxiv updated 2009/12/01

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 ∩_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 \citeBT2 and invariant measure considerations which allow us to obtain also precise large time dynamical informations on our solutions.

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