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.

引用

页码：1 / 19

页数：19

共 50 条

[31] Wave-breaking and weak instability for the stochastic modified two-component Camassa-Holm equations [J].

Zhao, Yongye ;

Li, Yongsheng ;

Chen, Fei .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2023, 74 (04)

[32] On the global attractor of the two-component π-Camassa-Holm equation with viscous terms [J].

Zong, Xiju ;

Sun, Shurong .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2014, 20 :82-98

[33] Criterion for Lyapunov stability of periodic Camassa-Holm equations [J].

Cao, Feng ;

Chu, Jifeng ;

Jiang, Ke .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2023, 202 (04) :1557-1572

[34] Equations of Camassa-Holm type and the geometry of loop groups [J].

Gorka, Przemyslaw ;

Pons, Daniel J. ;

Reyes, Enrique G. .

JOURNAL OF GEOMETRY AND PHYSICS, 2015, 87 :190-197

[35] Geometric approach on the global conservative solutions of the Camassa-Holm equation [J].

Lee, Jae Min .

JOURNAL OF GEOMETRY AND PHYSICS, 2019, 142 :137-150

[36] THE RELATION OF TWO-DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATIONS AND THE NAVIER-STOKES EQUATIONS [J].

杨灵娥 ;

纪艳珊 ;

郭柏灵 .

Acta Mathematica Scientia, 2009, 29 (01) :65-73

[37] On the Camassa-Holm and Hunter-Saxton equations [J].

Holden, H .

European Congress of Mathematics, 2005, :173-200

[38] Analytical Cartesian solutions of the multi-component Camassa-Holm equations [J].

An, Hongli ;

Hou, Liying ;

Yuen, Manwai .

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2019, 26 (02) :255-272

[39] Time periodic solution of the viscous Camassa-Holm equation [J].

Fu, YP ;

Guo, BL .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 313 (01) :311-321

[40] Nonlocal Symmetries of the Camassa-Holm Type Equations [J].

Lu Zhao ;

Changzheng Qu .

Chinese Annals of Mathematics, Series B, 2020, 41 :407-418

← 1 2 3 4 5 →