A stochastic variational approach to the viscous Camassa-Holm and Leray-alpha equations

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• 作者：Ana Bela Cruzeiro^a ; ^{abcruz@math.tecnico.ulisboa.pt} ; Guoping Liu^a ; ^b ; ^{liuguoping002@163.com}
• 关键词：Stochastic variational principles ; Camassa&ndash ; Holm equation ; Leray-alpha equations
• 刊名：Stochastic Processes and their Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：127
• 期：1
• 页码：1-19
• 全文大小：284 K
• 卷排序：127

文摘

We derive the (dd-dimensional) periodic incompressible and viscous Camassa–Holm equation as well as the Leray-alpha equations via stochastic variational principles. We discuss the existence of solution for these equations in the space H1H1 using the probabilistic characterization. The underlying Lagrangian flows are diffusion processes living in the group of diffeomorphisms of the torus. We study in detail these diffusions.