Steady motions of the Navier-Stokes fluid around a rotating body

Abstract

Consider the 3-dimensional Navier-Stokes fluid filling an infinite space exterior to a rotating body with constant angular velocity. By using the coordinate system attached to the body, the problem is reduced to an equivalent one in the fixed exterior domain. The reduced equation then involves an important drift operator, which is not subordinate to the usual Stokes operator and causes some difficulties. Based on [13], [26] and [12], this survey article addresses steady solutions to the reduced problem.