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

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  • T. Tachim Medjo

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.

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  • T. Tachim Medjo, 2023. "A stochastic Allen–Cahn–Navier–Stokes model with inertial effects driven by multiplicative noise of jump type," Mathematische Nachrichten, Wiley Blackwell, vol. 296(9), pages 4386-4428, September.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:9:p:4386-4428
    DOI: 10.1002/mana.202100492
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