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

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arxiv 1802.04000 v1 pith:T632SQKK submitted 2018-02-12 math.AP math.PRphysics.flu-dyn

Michele Coti Zelati , Nathan Glatt-Holtz , Konstantina Trivisa This is my paper · ORCID
classification math.APmath.PRphysics.flu-dyn
keywords compressibleinvariantmarkovnavier-stokesone-dimensionalsolutionsbehaviorbounds
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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.

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  1. Invariant Measures for Nonlinear Conservation Laws Driven by Stochastic Forcing

    math.AP 2019-08 reject novelty 6.0 of 10

    Existence and uniqueness of invariant measures are claimed for anisotropic degenerate parabolic-hyperbolic conservation laws driven by additive white noise, extending Debussche-Vovelle's first-order theory.

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