流体模型的随机分裂：遍历性与收敛性
Random Splitting of Fluid Models: Ergodicity and Convergence
AI总结：
本文提出一种将流体确定性动力学分解为基本向量场并随机切换的随机模型，证明其具有唯一平稳测度且在小噪声极限下几乎必然收敛到原模型，并成功应用于 Lorenz-96 方程及二维 Euler 和 Navier-Stokes 方程的 Galerkin 近似，且适用于保守动力学。
摘要：
我们引入一族随机模型，其动机来自对流体方程非平衡稳态的研究。这些模型将所关注的确定性动力学分解为基本构建块，即保留原始动力学某些基本方面的极小向量场。随机性通过依次沿每个向量场随机时长地跟随来注入。我们在一般假设下证明，这些随机动力学具有唯一的平稳测度，并在小噪声极限下几乎必然收敛到原始的确定性模型。我们将该构造应用于 Lorenz-96 方程（常用于混沌与数据同化研究）以及二维 Euler 方程和 Navier-Stokes 方程的 Galerkin 近似。所建立模型的一个有趣特征是，它们直接适用于保守动力学，而不仅仅适用于具有激励和耗散的动力学。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
