| Abstract: |
| In this talk, we present an existence and uniqueness result for a mathematical system which models the dynamics of an incompressible isothermal mixture of two immiscible Newtonian fluids flowing in a two- or three-dimensional bounded domain under stochastic perturbations. This model can be seen as a stochastic version of Navier-Stokes-Cahn-Hilliard model. In fact, the Navier-Stokes-Cahn-Hilliard model consists of the Navier-Stokes equations for the velocity, nonlinearly coupled with a convective nonlocal Cahn-Hilliard equation for the order (phase) parameter. We prove the existence of weak martingale solution for both 2D and 3D cases. In addition, we prove the existence of a unique (probabilistic) strong solution in two-dimensional bounded domain. |
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