MARKOV SELECTION FOR THE STOCHASTIC COMPRESSIBLE NAVIER-STOKES SYSTEM

• 成果类型: Article
• 署名作者: Breit, Dominic; Feireisl, Eduard; Hofmanova, Martina
• 署名单位: Heriot Watt University; Czech Academy of Sciences; Institute of Mathematics of the Czech Academy of Sciences; University of Bielefeld
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1566
• 发表日期: 2020
• 页码: 2547-2572
• 关键词: Ergodicity; EQUATIONS; driven

摘要

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.