On the existence and uniqueness of solution to a stochastic Chemotaxis–Navier–Stokes model

Erika Hausenblas, Boris Jidjou Moghomye and Paul André Razafimandimby

Stochastic Processes and their Applications, 2024, vol. 170, issue C

Abstract: In this article, we study a mathematical system modelling the dynamic of the collective behaviour of oxygen-driven swimming bacteria in an aquatic fluid flowing in a two dimensional bounded domain under stochastic perturbation. This model can be seen as a stochastic version of Chemotaxis–Navier–Stokes model. We prove the existence of a unique (probabilistic) strong solution. In addition, we establish some properties of the strong solution. More precisely, we prove that the unique solution is positive and satisfies the mass conservation property and an energy inequality.

Keywords: Navier–Stokes system; Chemotaxis; Stochastic; Probabilistic weak solution; Strong solution (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104274

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