Consider a body, B, rotating with constant angular velocity ω and fully submerged in a Navier-Stokes liquid that fills the whole space exterior to B. We analyze the flow of the liquid that is steady with respect to a frame attached to B. Our main theorem shows that the velocity field u of any weak solution (u 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+αas (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 ▶u and for the corresponding pressure field p. These results improve and clarify a recent result of R. Farwig and T. Hishida.
- Asymptotic behavior of solutions
- Navier-Stokes equations
- Rotating frame
ASJC Scopus subject areas