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arXiv · 1310.8353

Stochastically Symplectic Maps and Their Applications to Navier-Stokes Equation

Fraydoun Rezakhanlou
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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.

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Fraydoun Rezakhanlou. 2013-10-31. Stochastically Symplectic Maps and Their Applications to Navier-Stokes Equation. https://arxiv.org/abs/1310.8353

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