Stochastically Symplectic Maps and Their Applications to Navier-Stokes Equation
Probability
2013-11-01 v1
Abstract
Poincare's invariance principle for Hamiltonian flows implies Kelvin's principle for solution to Incompressible Euler Equation. Iyer-Constantin Circulation Theorem offers a stochastic analog of Kelvin's principle for Navier-Stokes Equation. Weakly symplectic diffusions are defined to produce stochastically symplectic flows in a systematic way. With the aid of symplectic diffusions, we produce a family of martigales associated with solutions to Navier-Stokes Equation that in turn can be used to prove Iyer-Constantin Circulation Theorem. We also review some basic facts in symplectic and contact geometry and their applications to Euler Equation.
Keywords
Cite
@article{arxiv.1310.8353,
title = {Stochastically Symplectic Maps and Their Applications to Navier-Stokes Equation},
author = {Fraydoun Rezakhanlou},
journal= {arXiv preprint arXiv:1310.8353},
year = {2013}
}