论文标题
随机Navier-Stokes方程的傅立叶模式的空间分析性和指数衰减
Spatial analyticity and exponential decay of Fourier modes for the stochastic Navier-Stokes equation
论文作者
论文摘要
我们构建了一个局部时间在空间上实现的解决方案到2D和3D随机Navier-由空间真实分析的乘法和运输噪声驱动的Stokes方程，但从初始条件中散发出来，仅需要具有有限的腹部。在该解决方案是全局时间的条件下，我们还建立了有限维盖金近似的指数衰减，相对于其最大波数，与随机Navier-stokes stokes方程的强路溶液相对于其最大波数。这种衰减在时间上是均匀的，相对于初始腹膜副本均匀，并且噪声系数均匀。
We construct a local in time spatially real-analytic solution to the 2D and 3D stochastic Navier--Stokes equation driven by a spatially real-analytic multiplicative and transport noise but emanating from an initial condition that is only required to have bounded enstrophy. Under the condition that the solution is global in time, we also establish the exponential decay of the finite-dimensional Galerkin approximation, with respect to its maximum wavenumber, to the strong pathwise solution of the stochastic Navier--Stokes equation. This decay is uniform in time, uniform with respect to the initial enstropy, and uniform in the noise coefficients.
