2022/09/14 by Lei Zhang, Bin Liu, Zhang, Lei +1
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2209.06500
openalex publication_date 2022/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the three-dimensional stochastic chemotaxis-Navier-Stokes (SCNS) system subjected to a Lévy-type random external force in bounded domain. Up to now, the existing results concerning global solvability of SCNS system mainly concentrated on the case of two spacial dimensions, little is known for the SCNS system in dimension three. We prove in present work that the three-dimensional SCNS system possesses at least one global martingale solution under proper assumptions, which is weak both in the analytical sense and in the stochastic sense. A new stochastic analogue of entropy-energy inequality and an uniform boundedness estimate are derived, which enable us to construct global-in-time approximate solutions from a properly regularized SCNS system via the Contraction Mapping Principle. The proof of the existence of martingale solution is based on the stochastic compactness method and an elaborate identification of the limits procedure, where the Jakubowski-Skorokhod Theorem is applied to deal with the phase spaces equipped with weak topology.