Random data Cauchy theory for nonlinear wave equations of power-type on ${\mathbb{R}}^3$

Abstract

We consider the defocusing nonlinear wave equation of power-type on ${\mathbb{R}}^3$. We establish an almost sure global existence result with respect to a suitable randomization of the initial data. In particular, this provides examples of initial data of super-critical regularity which lead to global solutions. The proof is based upon Bourgain's high-low frequency decomposition and improved averaging effects for the free evolution of the randomized initial data.

20 pages, 1 figure, typos corrected and minor changes. To appear in Comm. PDE

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Cited by in corpus (2)

• Invariant Gibbs Measure for 3D NLW in Infinite Volume
• Random data Cauchy theory for the fourth order nonlinear Schrödinger equation with cubic nonlinearity