Stochastic Euler-Poincaré reduction
Journal Article
·
· Journal of Mathematical Physics
- Institut de Mathématiques de Bordeaux (UMR 5251) Université Bordeaux 1 351, Cours de la Libération F33405 TALENCE Cedex (France)
- 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
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