Journal of Mathematical Fluid Mechanics

, Volume 14, Issue 4, pp 731–750 | Cite as

Continuity of Drag and Domain Stability in the Low Mach Number Limits

Article

Abstract

We consider a mathematical model of a rigid body immersed in a viscous, compressible fluid moving with a velocity prescribed on the boundary of a large channel containing the body. We assume that the Mach number is proportional to a small parameter ε and that the general boundary of the body contains small asperities of amplitude proportional to εα for a certain α > 0 and suppose the Navier’s slip condition on this rough boundary. We show that time averages of the drag functional converge, as ε → 0, to the corresponding time averages of the drag for the limit system, whereas the limit system is turning out to be the incompressible Navier–Stokes system with no-slip condition on the smooth limit body.

Mathematics Subject Classification (2010)

Primary 99Z99 Secondary 00A00 

Keywords

Navier–Stokes Low Mach limit Drag 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  2. 2.Department of Applied MathematicsIm Neuenheimer Feld 293HeidelbergGermany

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