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

被引：5

作者：

Cruzeiro, Ana Bela ^{[1
,2
]}

Liu, Guoping ^{[1
,2
,3
]}

机构：

[1] Inst Super Tecn UL, GFMUL, Ave Rovisco Pais, P-1049001 Lisbon, Portugal

[2] Inst Super Tecn UL, Dept Matemat, Ave Rovisco Pais, P-1049001 Lisbon, Portugal

[3] Chinese Acad Sci, AMSS, Zhongguancun East Rd 55, Beijing 100190, Peoples R China

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2017年 / 127卷 / 01期

关键词：

Stochastic variational principles; Camassa-Holm equation; Leray-alpha equations; SHALLOW-WATER EQUATION; DIFFEOMORPHISM GROUP; WELL-POSEDNESS; GEODESIC-FLOW; MODEL; DIFFUSIONS; TURBULENCE; EXISTENCE; MOTION; CIRCLE;

D O I：

10.1016/j.spa.2016.05.006

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We derive the (d-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 H-1 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. (C) 2016 Elsevier B.V. All rights reserved.

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页码：1 / 19

页数：19

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