论文标题
随机Navier-Stokes-$α$解决方案与随机Navier-Stokes Solutions的收敛
Convergence of the stochastic Navier-Stokes-$α$ solutions toward the stochastic Navier-Stokes solutions
论文作者
论文摘要
宽松地说，Navier-Stokes-$α$模型和Navier-Stokes方程式因由表示$α$的比例参数的空间过滤而异。从从强大的二维解决方案到由综合噪声驱动的Navier-Stokes-$α$模型开始，我们证明，在条件$α$下，它可以为随机的Navier-Stokes方程提供了强有力的解决方案。最初引入了概率空间，并且在整个调查中都可以在整个调查中维持了一个属于当地的属性的概率。高空间规律性在周期性边界条件下进行了流体速度矢量场的先验估计。
Loosely speaking, the Navier-Stokes-$α$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $α$. Starting from a strong two-dimensional solution to the Navier-Stokes-$α$ model driven by a multiplicative noise, we demonstrate that it generates a strong solution to the stochastic Navier-Stokes equations under the condition $α$ goes to 0. The initially introduced probability space and the Wiener process are maintained throughout the investigation, thanks to a local monotonicity property that abolishes the use of Skorokhod's theorem. High spatial regularity a priori estimates for the fluid velocity vector field are carried out within periodic boundary conditions.
