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- Title
Implications of Kunita–Itô–Wentzell Formula for k-Forms in Stochastic Fluid Dynamics.
- Authors
de Léon, Aythami Bethencourt; Holm, Darryl D.; Luesink, Erwin; Takao, So
- Abstract
We extend the Itô–Wentzell formula for the evolution of a time-dependent stochastic field along a semimartingale to k-form-valued stochastic processes. The result is the Kunita–Itô–Wentzell (KIW) formula for k-forms. We also establish a correspondence between the KIW formula for k-forms derived here and a certain class of stochastic fluid dynamics models which preserve the geometric structure of deterministic ideal fluid dynamics. This geometric structure includes Eulerian and Lagrangian variational principles, Lie–Poisson Hamiltonian formulations and natural analogues of the Kelvin circulation theorem, all derived in the stochastic setting.
- Subjects
FLUID dynamics; VARIATIONAL principles; STOCHASTIC processes; LAGRANGIAN mechanics; HAMILTONIAN systems; VECTOR fields
- Publication
Journal of Nonlinear Science, 2020, Vol 30, Issue 4, p1421
- ISSN
0938-8974
- Publication type
Article
- DOI
10.1007/s00332-020-09613-0