Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces

0506253 - MÚ 2020 RIV DE eng J - Článek v odborném periodiku
Breit, D. - Feireisl, Eduard - Hofmanová, M. - Maslowski, B.
Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces.
Probability Theory and Related Fields. Roč. 174, 3-4 (2019), s. 981-1032. ISSN 0178-8051. E-ISSN 1432-2064
GRANT EU: European Commission(XE) 320078 - MATHEF
Institucionální podpora: RVO:67985840
Klíčová slova: Navier–Stokes system * compressible fluid * stochastic perturbation * stationary solution
Obor OECD: Pure mathematics
Impakt faktor: 2.125, rok: 2019
Způsob publikování: Open access
http://dx.doi.org/10.1007/s00440-018-0875-4

We study the long-time behavior of solutions to a stochastically driven Navier–Stokes system describing the motion of a compressible viscous fluid driven by a temporal multiplicative white noise perturbation. The existence of stationary solutions is established in the framework of Lebesgue–Sobolev spaces pertinent to the class of weak martingale solutions. The methods are based on new global-in-time estimates and a combination of deterministic and stochastic compactness arguments. An essential tool in order to obtain the global-in-time estimate is the stationarity of solutions on each approximation level, which provides a certain regularizing effect. In contrast with the deterministic case, where related results were obtained only under rather restrictive constitutive assumptions for the pressure, the stochastic case is tractable in the full range of constitutive relations allowed by the available existence theory, due to the underlying martingale structure of the noise.
Trvalý link: http://hdl.handle.net/11104/0297555