A chemotaxis-fluid model driven by Lévy noise in ℝ²

2024/08/11 by Xu, Fan, Zhang, Lei, Liu, Bin
#Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2408.05685

Abstract

In this paper, we investigate the existence and uniqueness of global solutions to the Cauchy problem for a coupled stochastic chemotaxis-Navier-Stokes system with multiplicative Lévy noises in ℝ². The existence of global martingale solutions is proved under a framework that is based on the Faedo-Galerkin approximation scheme and stochastic compactness method, where the verification of tightness depends crucially on a novel stochastic version of Lyapunov functional inequality and proper compactness criteria in Fréchet spaces. A pathwise uniqueness result is also established with suitable assumption on the jump noises, which indicates that the considered system admits a unique global strong solution.

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