Open AccessOn weak martingale solutions to a stochastic Allen-Cahn-Navier-Stokes model with inertial effects
Author(s) -
T. Tachim Medjo
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021282
Subject(s) - martingale (probability theory) , mathematics , multiplicative function , bounded function , compact space , inertial frame of reference , lipschitz continuity , domain (mathematical analysis) , mathematical analysis , physics , quantum mechanics
We consider a stochastic Allen-Cahn-Navier-Stokes equations with inertial effects in a bounded domain \begin{document}$ D\subset\mathbb{R}^{d} $\end{document} , \begin{document}$ d = 2, 3 $\end{document} , driven by a multiplicative noise. The existence of a global weak martingale solution is proved under non-Lipschitz assumptions on the coefficients. The construction of the solution is based on the Faedo-Galerkin approximation, compactness method and the Skorokhod representation theorem.