Periodic measure for the stochastic equation of the barotropic viscous gas in a discretized one-dimensional domain
Rym Benseghir, Azzedine Benchettah, Paul Raynaud de Fitte · AIP conference proceedings · 2015
A stochastic equation system corresponding to the description of the motion of a barotropic viscous gas in a discretized one-dimensional domain with a weight regularizing the density is considered. In [2], the existence of an invariant measure was established for this discretized problem in the stationary case. In this paper, applying a slightly modified version of Khas'minskii's theorem [5], we generalize this result in the periodic case by proving the existence of a periodic measure for this problem.