粘性Camassa-Holm和Leray-alpha方程的随机变分方法
A stochastic variational approach to the viscous Camassa-Holm and Leray-alpha equations
摘要：
利用随机变分原理，导出了d维周期不可压粘性Camassa-Holm方程和Leray-alpha方程.利用概率刻画方法讨论了该方程在H1空间中解的存在性。基本的拉格朗日流是存在于环面的群同态中的扩散过程。我们详细研究这些扩散。
英文摘要：
We derive the (d-dimensional) periodic incompressible and viscous Camassa-Holm equation as well as the Leray-alpha equations via a stochastic variational principle. We discuss the existence of solution for this equation in the space H1 using the probabilistic characterisation. The underlying Lagrangian flows are diffusion processes living in the group of diffeomorphisms of the torus. We study in detail these diffusions.
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