On the stationary Navier-Stokes flows around a rotating body

Horst Heck, Hyunseok Kim, Hideo Kozono

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Consider the stationary motion of an incompressible Navier-Stokes fluid around a rotating body K = ℝ 3\Ω which is also moving in the direction of the axis of rotation. We assume that the translational and angular velocities U,ω are constant and the external force is given by f = div F. Then the motion is described by a variant of the stationary Navier-Stokes equations on the exterior domain Ω for the unknown velocity u and pressure p, with U, ω, F being the data. We first prove the existence of at least one solution (u, p) satisfying ∇u, p ∈ L 3/2,∞(Ω) and u ∈ L 3,∞(Ω) under the smallness condition on {pipe}U{pipe} + {pipe}ω{pipe} + {double pipe}F{double pipe} L3/2,∞(Ω). Then the uniqueness is shown for solutions (u, p) satisfying ∇u, p ∈ L 3/2,∞(Ω) ∩ L q,r(Ω) and u ∈ L 3,∞(Ω) ∩ L q*,r(Ω) provided that 3/2 < q < 3 and F ∈ L 3/2,∞(Ω) ∩ L q,r(Ω). Here L q,r(Ω) denotes the well-known Lorentz space and q* = 3q/(3 - q) is the Sobolev exponent to q.

Original languageEnglish
Pages (from-to)315-345
Number of pages31
JournalManuscripta Mathematica
Volume138
Issue number3-4
DOIs
Publication statusPublished - 2012 Jul
Externally publishedYes

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Stokes Flow
Navier-Stokes
Rotating
Stationary Navier-Stokes Equations
Incompressible Navier-Stokes
Lorentz Spaces
Motion
Exterior Domain
Angular velocity
Uniqueness
Exponent
Denote
Fluid
Unknown

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On the stationary Navier-Stokes flows around a rotating body. / Heck, Horst; Kim, Hyunseok; Kozono, Hideo.

In: Manuscripta Mathematica, Vol. 138, No. 3-4, 07.2012, p. 315-345.

Research output: Contribution to journalArticle

Heck, Horst ; Kim, Hyunseok ; Kozono, Hideo. / On the stationary Navier-Stokes flows around a rotating body. In: Manuscripta Mathematica. 2012 ; Vol. 138, No. 3-4. pp. 315-345.
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