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Symplectic Geometry and Navier-Stokes Equations

Mathematical 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.