Well-posedness for the stochastic electrokinetic flow

We investigate the stochastic electrokinetic flow modelled by a stochastic NernstPlanck-Navier-Stokes system with a blocking boundary conditions for ionic species concentrations in a smooth bounded domain D. In both 2D and 3D cases, we establish the global existence of weak martingale solution when the capacitance ς > 0, and also establish the existence of a unique maximal strong pathwise solution and a blow-up criterion when the capacitance ς = 0. In particular, we show that the maximal pathwise solution is global in 2D case without the restriction of smallness of initial data.

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