论文标题
液体模型的随机分裂：终点性和收敛性
Random Splitting of Fluid Models: Ergodicity and Convergence
论文作者
论文摘要
我们介绍了一个由流体方程的非平衡稳态的研究动机的随机模型家族。这些模型将兴趣的确定性动态分解为基本的构建基块，即，最小的矢量场保留了原始动力学的一些基本方面。随机遵循每个矢量场的随机量，将随机性注入。我们在一般的假设下表明，这些随机动力学具有独特的不变度度量，并且几乎可以肯定地融合到小噪声极限中的原始确定性模型。我们将构造应用于Lorenz-96方程，通常用于混乱和数据同化研究，以及2D Euler和Navier-Stokes方程的Galerkin近似值。开发的模型的一个有趣特征是，它们直接应用于保守的动态，而不仅仅是激发和耗散的动力学。
We introduce a family of stochastic models motivated by the study of nonequilibrium steady states of fluid equations. These models decompose the deterministic dynamics of interest into fundamental building blocks, i.e., minimal vector fields preserving some fundamental aspects of the original dynamics. Randomness is injected by sequentially following each vector field for a random amount of time. We show under general assumptions that these random dynamics possess a unique invariant measure and converge almost surely to the original, deterministic model in the small noise limit. We apply our construction to the Lorenz-96 equations, often used in studies of chaos and data assimilation, and Galerkin approximations of the 2D Euler and Navier-Stokes equations. An interesting feature of the models developed is that they apply directly to the conservative dynamics and not just those with excitation and dissipation.
