0 Ju l 2 00 7 RANDOM DATA CAUCHY THEORY FOR SUPERCRITICAL WAVE EQUATIONS II : A GLOBAL EXISTENCE RESULT
نویسندگان
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.
منابع مشابه
0 Ju l 2 00 7 RANDOM DATA CAUCHY THEORY FOR SUPERCRITICAL WAVE EQUATIONS I : LOCAL THEORY
— We study the local existence of strong solutions for the cubic nonlinear wave equation with data in H(M), s < 1/2, where M is a three dimensional compact riemannian manifold. This problem is supercritical and can be shown to be strongly ill-posed (in the Hadamard sense). However, after a suitable randomization, we are able to construct local strong solution for a large set of initial data in ...
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