Implications of Kunita-Ito-Wentzell Formula for k-Forms in Stochastic Fluid Dynamics

被引：13

作者：

de Leon, Aythami Bethencourt ^{[1
]}

Holm, Darryl D. ^{[1
]}

Luesink, Erwin ^{[1
]}

Takao, So ^{[1
]}

机构：

[1] Imperial Coll London, Math Dept, London, England

来源：

JOURNAL OF NONLINEAR SCIENCE | 2020年 / 30卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Stochastic geometric mechanics; Lie derivatives with respect to stochastic vector fields; Pull-back by smooth maps with stochastic time parameterization; LOCATION UNCERTAINTY; GEOPHYSICAL FLOWS; EQUATIONS;

D O I：

10.1007/s00332-020-09613-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We extend the Ito-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-Ito-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.

引用

页码：1421 / 1454

页数：34