Global well-posedness and interior regularity of 2D Navier–Stokes equations with stochastic boundary conditions

The paper is devoted to the analysis of the global well-posedness and the interior regularity of the 2D Navier-Stokes equations with inhomogeneous stochastic boundary conditions. The noise, white in time and coloured in space, can be interpreted as the physical law describing the driving mechanism on the atmosphere-ocean interface, i.e. as a balance of the shear stress of the ocean and the horizontal wind force.