Dissipative martingale solutions of the stochastically forced Navier–Stokes–Poisson system on domains without boundary. (February 2021)

• Record Type: Journal Article
• Authors: Donatelli, Donatella; Marcati, Pierangelo; Mensah, Prince Romeo
• Is Part Of: Nonlinear analysis. Volume 57(2021)
• Publication Date: 2021-02
• Subjects: Stochastic compressible fluid -- Navier–Stokes–Poisson system -- Weak martingale solution; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103201
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We construct solutions to the randomly-forced Navier–Stokes–Poisson system in periodic three-dimensional domains or in the whole three-dimensional Euclidean space. These solutions are weak in the sense of PDEs and also weak in the sense of probability. As such, they satisfy the system in the sense of distributions and the underlying probability space and the stochastic driving force are also unknowns of the problem. Additionally, these solutions dissipate energy, satisfies a relative energy inequality in the sense of Dafermos (1979) and satisfy a renormalized form of the continuity equation in the sense of DiPerna and Lions (1989).