3D steady compressible Navier--Stokes equations

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March 2008, 1(1): 151-163. doi: 10.3934/dcdss.2008.1.151

3D steady compressible Navier--Stokes equations

Milan Pokorný ^1, and Piotr B. Mucha ^2,

1.	Charles University Prague, Mathematical Institute, Sokolovská 83, 186 75 Praha, Czech Republic
2.	Warsaw University, Inst. of Applied Math. and Mech., ul. Banacha 2, 02-097 Warszawa, Poland

Received September 2006 Revised September 2007 Published December 2007

Abstract
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We study the steady compressible Navier--Stokes equations in a bounded smooth three-dimensional domain, together with the slip boundary conditions. We show that for a certain class of the pressure laws, there exists a weak solution with bounded density (in $L^\infty$ up to boundary).

Keywords: slip boundary conditions, steady compressible Navier--Stokes equations, existence and regularity of the solution..

Mathematics Subject Classification: Primary: 76N10; Secondary: 35Q3.

Citation: Milan Pokorný, Piotr B. Mucha. 3D steady compressible Navier--Stokes equations. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 151-163. doi: 10.3934/dcdss.2008.1.151

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