Low regularity solutions to a gently stochastic nonlinear wave equation in nonequilibrium statistical mechanics

TL;DR

This paper proves the global existence of low regularity solutions for a stochastic nonlinear wave equation modeling heat conduction, and establishes the existence of an invariant measure in thermal equilibrium.

Contribution

It introduces new methods to demonstrate global solutions in low regularity Sobolev spaces and constructs invariant measures for the system at equilibrium.

Findings

Global solutions exist in Sobolev spaces of low regularity

Invariant Gibbs measure exists at thermal equilibrium

Solutions extend below the energy norm threshold

Abstract

We consider a system of stochastic partial differential equations modeling heat conduction in a non-linear medium. We show global existence of solutions for the system in Sobolev spaces of low regularity, including spaces with norm beneath the energy norm. For the special case of thermal equilibrium, we also show the existence of an invariant measure (Gibbs state).