On the existence and uniqueness of solution to a stochastic 2D Allen-Cahn-Navier-Stokes model. (English) Zbl 1410.35295
Summary: We study, in this paper, a stochastic version of a coupled Allen-Cahn-Navier-Stokes model in a two-dimensional (2D) bounded domain. The model consists of the Navier-Stokes equations (NSEs) for the velocity, coupled with a Allen-Cahn model for the order (phase) parameter. We prove the existence and the uniqueness of a variational solution.
MSC:
| 35R60 | PDEs with randomness, stochastic partial differential 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 |
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