On the existence and uniqueness of solution to a stochastic chemotaxis-Navier-Stokes model. (English) Zbl 1534.35456
Summary: 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.
MSC:
| 35R60 | PDEs with randomness, stochastic partial differential equations |
| 35K51 | Initial-boundary value problems for second-order parabolic systems |
| 35K59 | Quasilinear parabolic equations |
| 35Q35 | PDEs in connection with fluid mechanics |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
| 86A05 | Hydrology, hydrography, oceanography |
| 92C17 | Cell movement (chemotaxis, etc.) |
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