Uniqueness of Dissipative Solutions to the Complete Euler System

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