Abstract
We consider the Navier–Stokes–Fourier system in a bounded domain \(\Omega \subset R^d\), \(d=2,3\), with physically realistic in/out flow boundary conditions. We develop a new concept of weak solutions satisfying a general form of relative energy inequality. The weak solutions exist globally in time for any finite energy initial data and comply with the weak–strong uniqueness principle.
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Notes
In what follows, we denote \({{\tilde{e}}}=e({{\tilde{\varrho }}},{{\tilde{\vartheta }}})\), \({{\tilde{p}}}=p({{\tilde{\varrho }}},{{\tilde{\vartheta }}})\) etc. if there is no danger of confusion.
In what follows, we denote \(a{\mathop {\sim }\limits ^{<}}b\) if there exists \(c>0\) independent of n, \(\varepsilon \), \(\delta \) such that \(a\le c b\).
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Communicated by A. Ionescu.
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The work of E.F. was supported by the Czech Sciences Foundation (GAČR), Grant Agreement 18-12719S.
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Feireisl, E., Novotný, A. Navier–Stokes–Fourier System with General Boundary Conditions. Commun. Math. Phys. 386, 975–1010 (2021). https://doi.org/10.1007/s00220-021-04091-1
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DOI: https://doi.org/10.1007/s00220-021-04091-1