Solvability of the 3D rotating Navier–Stokes equations coupled with a 2D biharmonic problem with obstacles and gradient restriction

A coupled system by the 3D rotating Navier–Stokes equations with a mixed boundary condition and a 2D biharmonic problem with two obstacles and the gradient restriction is investigated in this paper. Using the Schauder’s fixed point theorem, we show the existence of a strong solution for a sufficiently large viscosity ν and sufficiently small data.