Leading term at infinity of steady Navier-Stokes flow around a rotating obstacle

摘要

Consider a viscous incompressible flow around a body in rotating with constant angular velocity ω. Using a coordinate system attached to the body, the problem is reduced to a modified Navier-Stokes system in a fixed exterior domain. This paper addresses the question of the asymptotic behavior of stationary solutions to the new system as |x| → ∞. Under a suitable smallness assumption on the velocity field, u, and the net force on the boundary, N, we prove that the leading term of u is the so-called Landau solution U, a singular solution of the stationary Navier-Stokes system in with external force kωδ₀ and decaying as 1/|x|; here is a suitable constant determined by N and δ₀ is the Dirac measure supported in the origin.