L3-solutions for the stationary Navier-Stokes equations in the exterior of a rotating obstacle

Consider the stationary motion of an incompressible Navier-Stokes fluid around a rotating body R-3 \ Omega which is also moving in the direction of the axis of rotation with nonzero constant velocity -ke(1). We assume that the angular velocity omega = vertical bar omega vertical bar e(1) is also constant and the external force is given by f = divF. Then the motion is described by a variant of the stationary Navier-Stokes equations with the velocity kei at infinity. Our main result is the existence of at least one solution u satisfying u - ke(1) is an element of L-3(Omega) for arbitrarily large F is an element of L-3/2(Omega). The uniqueness is also proved by assuming that vertical bar omega vertical bar+vertical bar k vertical bar+parallel to F parallel to(L3/2) (Omega) is sufficiently small in comparison with the viscosity v. Moreover, we establish several regularity results to obtain an existence theorem for weak solutions u satisfying del u is an element of L-3/2(Omega) and u - k(e1) is an element of L-3 (Omega). (C) 2019 Published by Elsevier Ltd.