论文标题
具有随机强迫的等性Euler方程的独特性和能量平衡
Uniqueness and energy balance for isentropic Euler equation with stochastic forcing
论文作者
论文摘要
在本文中，我们证明了由圆柱维纳过程驱动的等质欧拉系统的唯一性和能量平衡。对于具有Hölder规律性$ C^α，α> 1/2 $的弱解的路径唯一性结果，并满足速度上的单方面Lipschitz。我们证明了带有随机强迫的等质Euler系统的Onsager猜想，即享有Hölder规律性$ C^α，α> 1/3 $的解决方案的能量平衡方程。这两个结果均通过考虑BESOV空间的规律性在更一般的环境中获得。
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 $C^α,α>1/2$ 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 $C^α,α>1/3$. Both the results have been obtained in a more general setting by considering regularity in Besov space.
