0 Ju l 2 00 7 RANDOM DATA CAUCHY THEORY FOR SUPERCRITICAL WAVE EQUATIONS II : A GLOBAL EXISTENCE RESULT
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چکیده
— 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<1/2H (Θ). We obtain this result as a consequence of a general random data Cauchy theory for supercritical wave equations developed in our previous work [6] and invariant measure considerations which allow us to obtain also precise large time dynamical informations on our solutions.
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0 Ju l 2 00 7 RANDOM DATA CAUCHY THEORY FOR SUPERCRITICAL WAVE EQUATIONS I : LOCAL THEORY
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تاریخ انتشار 2007