论文标题
通过随机强迫激发可压缩流体流的长时间行为
On the long time behavior of compressible fluid flows excited by random forcing
论文作者
论文摘要
我们关注随机Navier的长时间行为 - 在尺寸和三个方面，可压缩流体的stokes系统。在这种情况下，解决方案所占据的相空间的一部分取决于初始状态的选择。我们的主要结果是三倍。 （i）溶液的动能是普遍和渐近界的，与初始基准无关。 （ii）用最初控制能量的解决方案的时间偏移是渐近紧凑的，并生成针对R $中所有$ t \的整个解决方案。 （iii）每个具有最初控制能量的解决方案都会在其$ω$ - 限制设置的凸壳上关闭凸面上生成固定溶液，甚至产生固定的固定溶液。
We are concerned with the long time behavior of the stochastic Navier--Stokes system for compressible fluids in dimension two and three. In this setting, the part of the phase space occupied by the solution depends sensitively on the choice of the initial state. Our main results are threefold. (i) The kinetic energy of a solution is universally and asymptotically bounded, independent of the initial datum. (ii) Time shifts of a solution with initially controlled energy are asymptotically compact and generate an entire solution defined for all $t\in R$. (iii) Every solution with initially controlled energy generates a stationary solution and even an ergodic stationary solution on the closure of the convex hull of its $ω$--limit set.
