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Existence of weak solutions to the Navier-Stokes-Fourier system on Lipschitz domains. (English) Zbl 1163.35456

Summary: 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.

MSC:

35Q30 Navier-Stokes equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics