Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains

0340596 - MÚ 2010 RIV US eng C - Konferenční příspěvek (zahraniční konf.)
Poul, Lukáš
Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains.
Dynamical Systems and Differential Equations. Proceedings of the 6th AIMS International Conference. Springfield: American Institute of Mathematical Sciences, 2007 - (Belinskiy, B.; Lan., K.; Lu, X.), s. 834-843. ISBN 978-1-60133-010-9.
[6th AIMS International Conference. Poitiers (FR), 25.06.2006-28.06.2006]
Grant CEP: GA MŠMT LC06052
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: Navier-Stokes-Fourier system * weak solution * Lipschitz domain
Kód oboru RIV: BA - Obecná matematika

We prove existence of a weak solution to the Navier-Stokes-Fourier system on a bounded Lipschitz domain in R3. The key tool is the existence theory for weak solutions developed by Feireisl for the case of bounded smooth domains. We prove our result by inserting an additional limit passage where smooth domains approximate the Lipschitz one. Results on sensitivity of solutions with respect to the convergence of spatial domains are shortly discussed at the end of the paper.
Trvalý link: http://hdl.handle.net/11104/0183806