A stochastic Allen–Cahn–Navier–Stokes model with inertial effects driven by multiplicative noise of jump type

T. Tachim Medjo

Mathematische Nachrichten, 2023, vol. 296, issue 9, 4386-4428

Abstract: We consider a stochastic Allen–Cahn–Navier–Stokes equations with inertial effects and multiplicative noise of jump type in a bounded domain D⊂Rd$D\subset \mathbb {R}^{d}$, d=2,3$d=2,3$, 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.

Date: 2023
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https://doi.org/10.1002/mana.202100492

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