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.

中文翻译：

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具有一般边界条件的Navier–Stokes–Fourier系统

我们考虑在有界内/外流边界条件的有界域\（\ Omega \ subset R ^ d \），\（d = 2,3 \）中的Navier–Stokes–Fourier系统。我们提出了满足一般形式的相对能量不等式的弱解的新概念。对于任何有限的能量初始数据，弱解都会在全球范围内及时存在，并符合弱强关联的唯一性原则。