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

0349262 - MÚ 2011 RIV US eng J - Journal Article
Donatelli, D. - Feireisl, Eduard - Novotný, A.
On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions.
Discrete and Continuous Dynamical Systems-Series B. Roč. 13, č. 4 (2010), s. 783-798. ISSN 1531-3492. E-ISSN 1553-524X
R&D Projects: GA MŠMT LC06052; GA ČR GA201/08/0315
Institutional research plan: CEZ:AV0Z10190503
Keywords : Navier-Stokes equations * singular limits * low Mach number * compressible fluids * unbounded domains
Subject RIV: BA - General Mathematics
Impact factor: 0.874, year: 2010
http://www.aimsciences.org/journals/displayArticles.jsp?paperID=4976

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.
Permanent Link: http://hdl.handle.net/11104/0189549