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

Pages: 834 - 843, Issue Special, September 2007

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Lukáš Poul - Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic (email)

Abstract: We prove existence of a weak solution to the Navier-Stokes-Fourier system on a bounded Lipschitz domain in $\mathbb{R}^3$. 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.

Keywords:  Navier-Stokes-Fourier system, weak solutions, existence, Lipschitz domains.
Mathematics Subject Classification:  35Q30, 35A05, 76N10.

Received: September 2006;      Revised: June 2007;      Published: September 2007.