随机Navier-Stokes方程的半群分裂与立方体近似
Semigroup Splitting And Cubature Approximations For The Stochastic Navier-Stokes Equations
AI总结：
针对二维环面上随机Navier-Stokes方程的解的边际分布，采用高阶数值方法进行近似，通过分裂格式和Wiener空间上的立方体方法结合谱Galerkin离散化，获得了收敛速率并验证了方法的适用性。
摘要：
考虑在二维环面上随机Navier-Stokes方程的解的边际分布的高阶数值方法近似。对于分裂格式和应用于$N$次谱Galerkin离散化的Wiener空间上的立方体方法，获得了相应的收敛速率。虽然估计显示出强烈的$N$依赖性，但对于适当选择的时间步长，收敛得以实现。提供了数值模拟结果，并证实了这些方法的适用性。
英文摘要：
Approximation of the marginal distribution of the solution of the stochastic Navier-Stokes equations on the two-dimensional torus by high order numerical methods is considered. The corresponding rates of convergence are obtained for a splitting scheme and the method of cubature on Wiener space applied to a spectral Galerkin discretisation of degree $N$. While the estimates exhibit a strong $N$ dependence, convergence is obtained for appropriately chosen time step sizes. Results of numerical simulations are provided, and confirm the applicability of the methods.
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