Stationary solutions to the compressible Navier-Stokes system driven by stochastic forces
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Publication:2312686
DOI10.1007/S00440-018-0875-4zbMATH Open1447.35241arXiv1703.03177OpenAlexW2962858067WikidataQ129163711 ScholiaQ129163711MaRDI QIDQ2312686
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Publication date: 17 July 2019
Published in: (Search for Journal in Brave)
Abstract: 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. 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. This can be seen as a kind of regularizing effect of the noise on the global-in-time solutions.
Full work available at URL: https://arxiv.org/abs/1703.03177
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