Title: Higher-order synchronization for a nudging algorithm for the 2D Navier-Stokes equations with nodal observables
Abstract: The analytical study of a nudging algorithm in the infinite-dimensional setting of PDEs was initially carried out by Azouani, Olson, and Titi for the two-dimensional (2D) incompressible Navier-Stokes equations (NSE). In their seminal work, convergence of the approximating solution to the true solution was shown to take place in at least the Sobolev topology of functions with square-integrable, first-order weak derivatives; in 2D, however, this does not include uniform convergence. This talk will discuss convergence in stronger topologies, including the uniform topology, of this nudging-based algorithm for data assimilation in the context of the 2D NSE when observations are given as nodal values of the velocity field. This is joint work with Animikh Biswas (University of Maryland-Baltimore County) and Ken Brown (Hunter College).