On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions

Donatella Donatelli; Eduard Feireisl; Antonín Novotný

doi:10.3934/dcdsb.2010.13.783

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2010, Volume 13, Issue 4: 783-798. Doi: 10.3934/dcdsb.2010.13.783

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On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions

1.
Dipartimento di Matematica Pura ed Applicata, Università degli Studi dell'Aquila, Via Vetoio, 67010 Coppito (AQ)
2.
Institute of Mathematics AS ČR, Žitná 25, 115 67 Praha 1
3.
IMATH, Université du Sud Toulon-Var, BP 132, 839 57 La Garde

Received: April 2009

Revised: August 2009

Published: June 2010

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Abstract

We study the low Mach number limit for the compressible Navier-Stokes system supplemented with Navier's boundary condition on an unbounded domain with compact boundary. Our main result asserts that the velocities converge pointwise to a solenoidal vector field - a weak solution of the incompressible Navier-Stokes system - while the fluid density becomes constant. The proof is based on a variant of local energy decay property for the underlying acoustic equation established by Kato.

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Mathematics Subject Classification: Primary: 35Qxx; Secondary: 35D30, 76Nxx.

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On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions

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