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).

Dissipative martingale solutions of the stochastically forced Navier–Stokes–Poisson system on domains without boundary

Pierangelo Marcati
Supervision
;
Prince Romeo Mensah
Writing – Original Draft Preparation
2021

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).
Stochastic compressible fluid, Navier–Stokes–Poisson system,Weak martingale solution
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/15363
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