East Asian J. Appl. Math., 15 (2025), pp. 242-267.
Published online: 2025-01
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This paper considers a chemotaxis model coupled a stochastic Navier-Stokes equation in two-dimensional case. In non-convex bounded domain, it is proved that the stochastic chemotaxis-Navier-Stokes system possesses at least one global martingale weak solution when the chemotactic sensitivity function $\chi$ is nonsingular. In convex bounded domain, under the conditions of $\chi$ and per capita oxygen consumption rate $h$ are appropriately relaxed (where $\chi$ allows singularity), it is proved that the system admits a unique global mild solution. Our results generalize previously known ones.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-114.050224}, url = {http://global-sci.org/intro/article_detail/eajam/23749.html} }This paper considers a chemotaxis model coupled a stochastic Navier-Stokes equation in two-dimensional case. In non-convex bounded domain, it is proved that the stochastic chemotaxis-Navier-Stokes system possesses at least one global martingale weak solution when the chemotactic sensitivity function $\chi$ is nonsingular. In convex bounded domain, under the conditions of $\chi$ and per capita oxygen consumption rate $h$ are appropriately relaxed (where $\chi$ allows singularity), it is proved that the system admits a unique global mild solution. Our results generalize previously known ones.