Stochastic nonlinear wave dynamics on compact surfaces

Understand

We study the Cauchy problem for the nonlinear wave equations (NLW) with random data and/or stochastic forcing on a two-dimensional compact Riemannian manifold without boundary.

• (i) We first study the defocusing stochastic damped NLW driven by additive space-time white-noise, and with initial data distributed according to the Gibbs measure.
• By introducing a suitable space-dependent renormalization, we prove local well-posedness of the renormalized equation.
• Bourgain's invariant measure argument then allows us to establish almost sure global well-posedness and invariance of the Gibbs measure for the renormalized stochastic damped NLW.