Invariant measures for the stochastic one-dimensional compressible\n Navier-Stokes equations

2018/02/12 by Michele Coti Zelati, Zelati, Michele Coti, Nathan Glatt-Holtz +3
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1802.04000

openalex publication_date 2018/02/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the long-time behavior of solutions to a stochastically forced\none-dimensional Navier-Stokes system, describing the motion of a compressible\nviscous fluid, in the case of linear pressure law. We prove existence of an\ninvariant measure for the Markov process generated by strong solutions. We\novercome the difficulties of working with non-Feller Markov semigroups on\nnon-complete metric spaces by generalizing the classical Krylov-Bogoliubov\nmethod, and by providing suitable polynomial and exponential moment bounds on\nthe solution, together with pathwise estimates.\n

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