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

Lukáš Poul

doi:10.3934/proc.2007.2007.834

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2007, Volume 2007: 834-843. Doi: 10.3934/proc.2007.2007.834 open access

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

Lukáš Poul^1,

1.
Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1

Received: August 31, 2006

Revised: May 31, 2007

Published: August 2007

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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.

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Mathematics Subject Classification: 35Q30, 35A05, 76N10.

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

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