Events for 10/27/2020 from all calendars

Nonlinear Partial Differential Equations

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Michael Jolly, Indiana University

Title: Data assimilation for the 2D Navier-Stokes equations using local observables

Abstract: We will discuss an approximate, global data assimilation/synchronization algorithm based on purely local observations for the two-dimensional Navier-Stokes equations on the torus. We will present a rigorous result stating that, for any error threshold, if the reference flow is analytic with sufficiently large analyticity radius, then it can be recovered within that threshold. We will then show the result of numerical tests of the effectiveness of this approach, as well as variants with data on moving subdomains. In particular, computations demonstrate that machine precision synchronization is achieved for mobile data collected from a small fraction of the domain. This is joint work with Animikh Biswas and Zachary Bradshaw.