Asymptotic structure of a Leray solution to the Navier–Stokes flow around a rotating body

Abstract

Consider a body, Ꮾ, rotating with constant angular velocity ω and fully submerged in a Navier-Stokes liquid that fills the whole space exterior to Ꮾ.We analyze the flow of the liquid that is steady with respect to a frame attached to Ꮾ.Our main theorem shows that the velocity field v of any weak solution (v, p) in the sense of Leray has an asymptotic expansion with a suitable Landau solution as leading term and a remainder decaying pointwise like 1/|x| 1+α as |x| → ∞ for any α ∈ (0, 1), provided the magnitude of ω is below a positive constant depending on α.We also furnish analogous expansions for ∇v and for the corresponding pressure field p.These results improve and clarify a recent result of R. Farwig and T. Hishida.