Open Access
December 2020 Markov selection for the stochastic compressible Navier–Stokes system
Dominic Breit, Eduard Feireisl, Martina Hofmanová
Ann. Appl. Probab. 30(6): 2547-2572 (December 2020). DOI: 10.1214/20-AAP1566


We analyze the Markov property of solutions to the compressible Navier–Stokes system perturbed by a general multiplicative stochastic forcing. We show the existence of an almost sure Markov selection to the associated martingale problem. Our proof is based on the abstract framework introduced in Flandoli and Romito (Probab. Theory Related Fields 40 (2008) 407–458). A major difficulty arises from the fact, different from the incompressible case, that the velocity field is not continuous in time. In addition, it cannot be recovered from the variables whose time evolution is described by the Navier–Stokes system, namely, the density and the momentum. We overcome this issue by introducing an auxiliary variable into the Markov selection procedure.


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Dominic Breit. Eduard Feireisl. Martina Hofmanová. "Markov selection for the stochastic compressible Navier–Stokes system." Ann. Appl. Probab. 30 (6) 2547 - 2572, December 2020.


Received: 1 September 2018; Revised: 1 October 2019; Published: December 2020
First available in Project Euclid: 14 December 2020

Digital Object Identifier: 10.1214/20-AAP1566

Primary: 35Q30 , 60H15 , 60H30 , 76M35 , 76N10

Keywords: compressible Navier–Stokes system , Markov selection , martingale solution , stochastic forcing

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.30 • No. 6 • December 2020
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