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Symplectic Geometry and Navier-Stokes EquationsMathematical Physics & Probability
|Speaker: ||Fraydoun Rezakhanlou, UC Berkeley|
|Location: ||1147 MSB|
|Start time: ||Wed, Oct 2 2013, 4:10PM|
Flows can be defined for diffusions with sufficiently regular
coefficients. Using stochastic calculus one can decide whether or not a diffusion produces a symplectic flow. However, it is much easier for the flow of a diffusion to be weakly symplectic i.e. the associated symplectic form is invariant in some averaged sense. Iyer-Constantin Circulation Theorem is a stochastic analog of Kelvin's principle for Navier-Stokes Equation. With the aid of symplectic diffusions, one can produce various martingales associated with solutions to Navier-Stokes Equation.