Dissipative solutions have recently been studied as a generalized concept for weak solutions of the complete Euler system. Apparently, these are expectations of suitable measure valued solutions. Motivated from Feireisl et al. (Commun Partial Differ Equ 44(12):1285–1298, 2019), we impose a one-sided Lipschitz bound on velocity component as uniqueness criteria for a weak solution in Besov space \(B^{\alpha ,\infty }_{p}\) with \(\alpha >1/2\). We prove that the Besov solution satisfying the above mentioned condition is unique in the class of dissipative solutions. In the later part of this article, we prove that the one sided Lipschitz condition gives uniqueness among weak solutions with the Besov regularity, \(B^{\alpha ,\infty }_{3}\) for \(\alpha >1/3\). Our proof relies on commutator estimates for Besov functions and the relative entropy method.

最近，耗散解已作为完整Euler系统的弱解的广义概念进行了研究。显然，这些都是对合适的度量值解决方案的期望。源自Feireisl等。（公共部分差分方程44（12）：1285-1298，2019年），我们在速度分量上施加了一个单侧Lipschitz边界作为Besov空间\（B ^ {\ alpha，\ infty} _中的一个弱解的唯一性准则{p} \）和\（\ alpha> 1/2 \）。我们证明了满足上述条件的Besov解决方案在耗散解决方案类别中是唯一的。在本文的后面的部分中，我们证明了一个单边Lipschitz条件给出与的Besov规律性弱解，其中唯一\（B ^ {\α，\ infty} _ {3} \）为\（\ alpha> 1/3 \）。我们的证明依赖于Besov函数的换向子估计和相对熵方法。