On the stationary Navier-Stokes flows around a rotating body

초록

Consider the stationary motion of an incompressible Navier-Stokes fluid around a rotating body which is also moving in the direction of the axis of rotation. We assume that the translational and angular velocities , are constant and the external force is given by = div . Then the motion is described by a variant of the stationary Navier-Stokes equations on the exterior domain Omega for the unknown velocity and pressure , with , , being the data. We first prove the existence of at least one solution (, ) satisfying and under the smallness condition on . Then the uniqueness is shown for solutions (, ) satisfying and provided that 3/2 < < 3 and . Here (Omega) denotes the well-known Lorentz space and * = 3 /(3 - ) is the Sobolev exponent to .

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