Stochastic Euler-Poincaré reduction

Journal Article · Fri Aug 15 00:00:00 EDT 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4893357· OSTI ID:22306025

Arnaudon, Marc ^[1]; Chen, Xin ^[2]

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1. Institut de Mathématiques de Bordeaux (UMR 5251) Université Bordeaux 1 351, Cours de la Libération F33405 TALENCE Cedex (France)
2. Grupo de Física-Matemática Univ. Lisboa, Av.Prof. Gama Pinto 2 1649-003 Lisboa (Portugal)

We prove a Euler-Poincaré reduction theorem for stochastic processes taking values on a Lie group, which is a generalization of the reduction argument for the deterministic case [J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems, Texts in Applied Mathematics (Springer, 2003)]. We also show examples of its application to SO(3) and to the group of diffeomorphisms, which includes the Navier-Stokes equation on a bounded domain and the Camassa-Holm equation.

• OSTI ID: 22306025
• Journal Information: Journal of Mathematical Physics, Vol. 55, Issue 8; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CLASSICAL MECHANICS
LIE GROUPS
NAVIER-STOKES EQUATIONS
STOCHASTIC PROCESSES
SYMMETRY