Nonlinear Partial Differential Equations : the Abel Symposium 2010

0369966 - MÚ 2012 RIV DE eng M - Monography Chapter
Feireisl, Eduard - Schonbek, M.E.
On the Oberbeck-Boussinesq approximation on unbounded domains.
Nonlinear Partial Differential Equations : the Abel Symposium 2010. Berlin: Springer, 2012 - (Holden, H.; Karlsen, K.), s. 131-168. Abel Symposia, 7. ISBN 978-3-642-25360-7
R&D Projects: GA ČR GA201/09/0917
Institutional research plan: CEZ:AV0Z10190503
Keywords : Oberbeck-Boussinesq system * singular limit * unbounded domain
Subject RIV: BA - General Mathematics
http://link.springer.com/chapter/10.1007/978-3-642-25361-4_7

We study the Oberbeck-Boussinesq approximation describing the motion of an incompressible, heat-conducting fluid occupying a general unbounded domain in R3. We provide a rigorous justification of the model by means of scale analysis of the full Navier-Stokes-Fourier system in the low Mach and Froude number regime on large domains, the diameter of which is proportional to the speed of sound. Finally, we show that the total energy of any solution of the resulting Oberbeck-Boussinesq system tends to zero with growing time.
Permanent Link: http://hdl.handle.net/11104/0203901