Jonathan Mattingly - Duke University
Wednesday, April 20, 10:45AM (Zoom meeting starts at 10:30)
“A random forcing model of the 2D fluid equations”
Abstract: The Navier-Stokes and Euler equations describe the flow of a incompressible fluid, respectively with and without viscous effects. When interested in out-of-equilibrium effects such as turbulence one often needs to add external forcing to the system. Such forcing can serve multiple roles. (1) It can inject energy into the system to offset dissipative effects. (2) it can prescribe a particular structure at a particular scale, and (3) keep the system in a “generic state” by regularly providing perturbations. The later is important when one wants to talk about the statistical properties of the system for which ergodicity is often central
I will discuss a new way to introduce stochasticity into the 2D Euler and Navier Stokes equation which is designed to better separate the three roles of the forcing above. the It is based on a randomized splitting scheme. I will discuss various longtime properties such as unique ergodicity and Lyapunov exponents in the context of finite dimensional approximations of these systems