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

Abstract

Consider a viscous incompressible flow around a body in \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb R^3$\end{document} 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 \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb R^3$\end{document} with external force kωδ0 and decaying as 1/|x|; here \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$k\in \mathbb R$\end{document} is a suitable constant determined by N and δ0 is the Dirac measure supported in the origin.