论文标题
千古的理论，用于能量开放的可压缩流体流动
Ergodic theory for energetically open compressible fluid flows
论文作者
论文摘要
检查了由正压Navier代表的能量开放的流体系统检查的奇异假说 - 具有一般流入/流出边界条件的Stokes方程。我们表明，任何全球界限的轨迹都会生成固定统计解决方案，该解决方案被解释为一个随机过程，其连续轨迹由问题的弱解决方案家族支持。将抽象的Birkhoff - Khinchin定理应用于获得（在预期和A.S.中）的收敛（在任何有界的硼孔）中，以获得与任何固定溶液相关的状态变量的可测量函数。最后，我们表明，沿着整个解决方案的行为（即针对r $中的任何$ t \定义的解决方案）确定了厄基德假设的有效性。特别是，对于任何轨迹，提供其轨迹空间中设置的$ω-$限制的任何轨迹的平均值都支持独特的（法律）固定解决方案。
The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier--Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a stationary statistical solution, which is interpreted as a stochastic process with continuous trajectories supported by the family of weak solutions of the problem. The abstract Birkhoff--Khinchin theorem is applied to obtain convergence (in expectation and a.s.) of ergodic averages for any bounded Borel measurable function of state variables associated to any stationary solution. Finally, we show that validity of the ergodic hypothesis is determined by the behavior of entire solutions (i.e. a solution defined for any $t\in R$). In particular, the ergodic averages converge for any trajectory provided its $ω-$limit set in the trajectory space supports a unique (in law) stationary solution.
