In this paper, we consider a compressible dissipative Baer–Nunziato-type system for a mixture of two compressible heat conducting gases. We prove that the set of weak solutions is stable, meaning that any sequence of weak solutions contains a (weakly) convergent subsequence whose limit is again a weak solution to the original system. Such type of results is usually considered as the most essential step to the proof of the existence of weak solutions. This is the first result of this type in the mathematical literature. Nevertheless, the construction of weak solutions to this system however remains still an (difficult) open problem.

中文翻译：

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两种可压缩导热气体混合物的耗散 Baer-Nunziato 型系统的弱解

在本文中，我们考虑了一种可压缩耗散 Baer-Nunziato 型系统，用于两种可压缩导热气体的混合物。我们证明弱解集是稳定的，这意味着任何弱解序列都包含一个（弱）收敛子序列，其极限再次是原始系统的弱解。这种类型的结果通常被认为是证明弱解存在的最重要的一步。这是数学文献中这种类型的第一个结果。然而，该系统的弱解决方案的构建仍然是一个（困难的）开放问题。