MHD flow with Navier type boundary conditions

Abstract

We are concerned here with results of existence and regularity of solutions to a stationary MHD problem, with a possibly multi-connected 2D domain associated with Navier-type boundary conditions. The RHS f, corresponding to the external forces, is in Lp(Ω), with p≥2, without any restriction on its norm. Two main difficulties are encountered in solving these problems: the geometry of the domain and the non-linear term (u⋅∇)(u−αΔu). We prove the existence of a solution (u,B) in H2(Ω)×W2,r(Ω) for any finite r.