Let \({\mathcal {S}} = \{ \tau _n \}_{n=1}^\infty \subset (0,T)\) be an arbitrary countable (dense) set. We show that for any given initial density and momentum, the compressible Euler system admits (infinitely many) admissible weak solutions that are not strongly continuous at each \(\tau _n\), \(n=1,2,\dots \). The proof is based on a refined version of the oscillatory lemma of De Lellis and Székelyhidi with coefficients that may be discontinuous on a set of zero Lebesgue measure.

中文翻译：

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关于可压缩欧拉系统的弱解的强连续性

令\（{\ mathcal {S}} = \ {\ tau _n \} _ {n = 1} ^ \ infty \ subset（0，T）\）为任意可数（密集）集合。我们表明，对于任何给定的初始密度和动量，可压缩的Euler系统都允许（无限多个）可容许的弱解，这些弱解在每个\（\ tau _n \），\（n = 1,2，\ dots \）上都不是强连续的。证明基于De Lellis和Székelyhidi的振荡引理的改进版本，其系数在一组零Lebesgue测度上可能是不连续的。