TY - JOUR

T1 - Asymptotic structure of a leray solution to the navier-stokes flow around a rotating body

AU - Farwig, Reinhard

AU - Galdi, Giovanni P.

AU - Kyed, Mads

N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - Asymptotic behavior of solutions

KW - Navier-Stokes equations

KW - Rotating frame

UR - http://www.scopus.com/inward/record.url?scp=84858409524&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84858409524&partnerID=8YFLogxK

U2 - 10.2140/pjm.2011.253.367

DO - 10.2140/pjm.2011.253.367

M3 - Article

AN - SCOPUS:84858409524

VL - 253

SP - 367

EP - 382

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 2

ER -