论文标题
关于不可压缩流体的随机方程的弱唯一性
On weak-strong uniqueness for stochastic equations of incompressible fluid flow
论文作者
论文摘要
我们将耗散度量值的martingale解决方案的新颖概念引入了描述不可压缩流体运动的随机欧拉方程。这些解决方案的特征是总能量平衡中的参数化年轻度量和浓度缺陷度量。此外，它们在概率意义上是弱的，即潜在的概率空间和驱动维纳过程是解决方案的内在部分。在与现有文献的显着背离中，我们首先表现出由乘法噪声驱动的不可压缩的欧拉方程的相对能量不等式，然后展示了路径方向弱的唯一性原理。最后，我们还提供了足够的条件，即La Prodi和serrin，以使弱的Martingale解决方案在有限的能量弱的Martingale解决方案中对随机Naiver-Stokes系统的独特性。
We introduce a novel concept of dissipative measure-valued martingale solution to the stochastic Euler equations describing the motion of an inviscid incompressible fluid. These solutions are characterized by a parametrized Young measure and a concentration defect measure in the total energy balance. Moreover, they are weak in the probablistic sense i.e., the underlying probablity space and the driving Wiener process are intrinsic part of the solution. In a significant departure from the existing literature, we first exhibit the relative energy inequality for the incompressible Euler equations driven by a multiplicative noise, and then demonstrate pathwise weak-strong uniqueness principle. Finally, we also provide a sufficient condition, a la Prodi and Serrin, for the uniqueness of weak martingale solutions to stochastic Naiver-Stokes system in the class of finite energy weak martingale solutions.
