|Date: Friday, November 18, 2016
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: Determining forms and data assimilation
Abstract: A determining form for a dissipative PDE is an ODE in a certain trajectory space where the solutions on the global attractor of the PDE are readily recognized. It is an ODE in the true sense of defining a vector field which is (globally) Lipschitz. In this talk we focus on one type of determining form where solutions on the global attractor of the PDE are identified as steady states of the form. This determining form is related to data assimilation by feedback nudging, which is one way to inject a coarse-grain time series into the model in order to recover the matching full solution. We show that for a given initial trajectory, the dynamics of this determining form reduces to that of a one-dimensional ODE. We prove lower bounds on the rates of convergence to trajectories in the attractor of the original system, and demonstrate numerically that they are achieved. Applications have been made to the 2D incompressible Navier-Stokes, damped-driven nonlinear Schroedinger, damped-driven Korteweg-de Vries and surface quasigeostrophic equations.
Speaker: Michael Jolly
Institution: Indiana University
Event Organizer: Charlie Doering firstname.lastname@example.org