Mike Jolly : Determining forms and data assimilation

Posted by Mimi Dai , part of the Departmental Colloquium.

At

Feb. 24, 2017, 3 p.m.

In

SEO 636

Abstract

A determining form for a dissipative partial differential equation is an ordinary differential equation 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. We discuss two types of determining forms: one where solutions on the global attractor of the PDE are traveling waves, and another where they are steady states. Each determining form is related to a certain approach to data assimilation, i.e. the injection of a coarse-grain time series into the model in order to recover the matching full solution. Applications have been made to the 2D incompressible Navier-Stokes, damped-driven nonlinear Schrodinger, damped-driven Korteveg-de Vries and surface quasigeostrophic equations.