On the Asymptotic Behavior of Physically Reasonable Solutions to the Stationary Navier—Stokes System in Three-dimensional Exterior Domains with Zero Velocity at Infinity

Abstract

We consider physically reasonable solutions of the stationary Navier—Stokes system in a three-dimensional exterior domains with zero velocity at infinity. We show that when these solutions are asymptotically expanded near infinity, the leading term cannot be the product of a non-zero vector with the Stokes fundamental solution. This result should be contrasted with the case when the velocity at infinity is not zero. Then, as is well known, such an expansion is possible, with the leading term being the product of a suitable constant vector with the fundamental Oseen solution.