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
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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 -