Abstract The dissipative solutions can be seen as a convenient generalization of the concept of weak solution to the isentropic Euler system. They can be seen as expectations of the Young measures associated to a suitable measure-valued solution of the problem. We show that dissipative solutions coincide with weak solutions starting from the same initial data on condition that: (i) the weak solution enjoys certain Besov regularity; (ii) the symmetric velocity gradient of the weak solution satisfies a one-sided Lipschitz bound.

中文翻译：

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等熵欧拉系统耗散解的唯一性

摘要 耗散解可以看作是等熵欧拉​​系统弱解概念的一种方便的推广。它们可以被看作是对与问题的合适的度量值解决方案相关联的 Young 度量的期望。我们证明耗散解与从相同初始数据开始的弱解一致，条件是：（i）弱解具有一定的 Besov 规律；(ii) 弱解的对称速度梯度满足单边 Lipschitz 界。