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Invariant Measures for the Stochastic One-Dimensional Compressible Navier-Stokes Equations.

Appl Math Optim 2021 16;83(3):1487-1522. Epub 2019 Jul 16.

Department of Mathematics, University of Maryland, College Park, MD 20742 USA.

We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an invariant measure for the Markov process generated by strong solutions. We overcome the difficulties of working with non-Feller Markov semigroups on non-complete metric spaces by generalizing the classical Krylov-Bogoliubov method, and by providing suitable polynomial and exponential moment bounds on the solution, together with pathwise estimates. Read More

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