Invariant Gibbs dynamics for the hyperbolic sinh-Gordon model

Whilst there has a been a wealth of progress on random dispersive equations with polynomial nonlinearities, the non-polynomial case remains much less developed. In this talk, I will discuss recent progress, on the well-posedness (and invariance of the Gibbs measure) for the two-dimensional stochastic periodic damped Klein-Gordon equation with exponential-type nonlinearities; a setting which covers the so-called hyperbolic Liouville and hyperbolic sinh-Gordon models. We develop a novel physical space framework for wave equations with non-negative and non-polynomial nonlinearities, which goes beyond the traditional \(L^2\)-framework, and obtain the first results for the hyperbolic sinh-Gordon model and improved results for the hyperbolic Liouville model.

This is joint work with Y. Zine (EPFL)