Invariant Gibbs measure evolution for the radial nonlinear wave equation on the 3d ball

Abstract

We establish new global well-posedness results along Gibbs measure evolution for the nonlinear wave equation posed on the unit ball in R3 via two distinct approaches. The first approach invokes the method established in the works Bourgain (1994, 1996) [3–5] based on a contraction-mapping principle and applies to a certain range of nonlinearities. The second approach allows to cover the full range of nonlinearities admissible to treatment by Gibbs measure, working instead with a delicate analysis of convergence properties of solutions. The method of the second approach is quite general, and we shall give applications to the nonlinear Schrödinger equation on the unit ball in subsequent works Bourgain and Bulut (2013) [10,11].