Strand II Mini-Course: The Stochastic Navier-Stokes equations

Strand II Mini-Course: The Stochastic Navier-Stokes equations (February 16 to March 24)

Instructor

Jonathan Mattingly

Description

I will teach a mini-course on the Ergodic theory of the Stochastic Navier-Stokes equations. The course will start with an introduction to stochastic differential equations and stochastic partial differential equationsin general through the stochastic Navier-Stokes equations. We will then talk about invariant measure and random attractors and some elements of ergodic theory. This will be followed by an introduction to mixing and the ergodic properties of stochastic differential equations (both elliptic and hypo-elliptic). Lastly how to extend these ideas to prove ergodic results about the stochastic Navier-Stokes equations. Thorough out the course the stochastic Navier-Stokes equations will be used as a model problem. However the ideas will be applicable to many stochastically forced dissipative dynamical system; especially in infinite dimensions.

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Last modified October 29, 2004