Markov selection for the stochastic compressible Navier-Stokes system

0536683 - MÚ 2021 RIV US eng J - Článek v odborném periodiku
Breit, D. - Feireisl, Eduard - Hofmanová, M.
Markov selection for the stochastic compressible Navier-Stokes system.
Annals of Applied Probability. Roč. 30, č. 6 (2020), s. 2547-2572. ISSN 1050-5164
Grant CEP: GA ČR(CZ) GA18-05974S
Institucionální podpora: RVO:67985840
Klíčová slova: compressible Navier-Stokes system * Markov selection * Martingale solution * stochastic forcing
Obor OECD: Pure mathematics
Impakt faktor: 1.872, rok: 2020
Způsob publikování: Omezený přístup
https://dx.doi.org/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.
Trvalý link: http://hdl.handle.net/11104/0314412