论文标题
$α$ -NAVIER-Stokes方程式由Trace类的时空噪声扰动
$α$-Navier-Stokes equation perturbed by space-time noise of trace class
论文作者
论文摘要
我们考虑$α$ -Navier-Stokes模型的随机扰动。随机扰动是跟踪类的加性时空噪声。在噪音前面的操作员$ q $的痕迹的自然条件下，我们证明了强大解决方案的存在和独特性，在$ l^{2} $函数的经典空间中连续及时及时，具有非线性项的估计值。它基于对有限维系统解决方案的先验估计以及近似溶液的紧密度。 此外，通过研究溶液在初始数据方面的衍生物，我们可以证明近似溶液的指数力矩，足以获得强大的偶性特性和过渡半群的不可约性。这自然导致了不变措施的存在和独特性。
We consider a stochastic perturbation of the $α$-Navier-Stokes model. The stochastic perturbation is an additive space-time noise of trace class. Under a natural condition about the trace of operator $Q$ in front of the noise, we prove the existence and uniqueness of strong solution, continuous in time in classical spaces of $L^{2}$ functions with estimates of non-linear terms. It is based on a priori estimate of solutions of finite-dimensional systems, and tightness of the approximated solution. Moreover, by studying the derivative of the solution with respect to the initial data, we can prove exponential moment of the approximated solutions, which is enough to obtain Strong Feller property and irreducibility of the transition semigroup. This leads naturally to the existence and uniqueness of an invariant measure.
