Archive for Rational Mechanics and Analysis

, Volume 200, Issue 1, pp 21–58 | Cite as

Steady-State Navier–Stokes Flows Past a Rotating Body: Leray Solutions are Physically Reasonable

  • Giovanni P. Galdi
  • Mads KyedEmail author


A rigid body, \({\fancyscript{B}}\), moves in a Navier–Stokes liquid, \({\fancyscript{L}}\), filling the whole space outside \({\fancyscript{B}}\). We assume that, when referred to a frame attached to \({\fancyscript{B}}\), the nonzero velocity of the center of mass, ξ, and the angular velocity, ω, of \({\fancyscript{B}}\) are constant and that the flow of \({\fancyscript{L}}\) is steady. Our main theorem implies that every “weak” steady-state solution in the sense of Leray is, in fact, physically reasonable in the sense of Finn, for data of arbitrary “size”. Such a theorem improves and generalizes an analogous famous result of Babenko (Math USSR Sb 20:1–25, 1973), obtained in the case ω = 0.


Rigid Body Stokes Equation Inertial Frame Exterior Domain Cubature Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Materials ScienceUniversity of PittsburghPittsburghUSA
  2. 2.Institut für MathematikRWTH-AachenAachenGermany

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