In this article, we prove uniqueness and energy balance for isentropic Euler system driven by a cylindrical Wiener process. Pathwise uniqueness result is obtained for weak solutions having Hölder regularity $C^{\alpha },\alpha >1∕2$ in space and satisfying one-sided Lipschitz bound on velocity. We prove Onsager’s conjecture for isentropic Euler system with stochastic forcing, that is, energy balance equation for solutions enjoying Hölder regularity $C^{\alpha },\alpha >1∕3$. Both the results have been obtained in a more general setting by considering regularity in Besov space.

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具有随机强迫的等熵Euler方程的唯一性和能量平衡

在本文中，我们证明了圆柱维纳过程驱动的等熵Euler系统的唯一性和能量平衡。对于具有Hölder正则性的弱解获得路径唯一性结果$C^{\alpha }，\alpha >\mathrm{1个}∕\mathrm{2个}$在空间上，并满足速度方面的令人满意的Lipschitz约束。我们证明了具有随机强迫的等熵Euler系统的Onsager猜想，即具有Hölder正则性的解决方案的能量平衡方程$C^{\alpha }，\alpha >\mathrm{1个}∕3$。通过考虑Besov空间中的规则性，可以在更一般的环境中获得这两个结果。