Edriss Titi (Texas A&M University, USA)
One of the main characteristics of infinite-dimensional dissipative evolution equations, such as the Navier-Stokes equations and reaction-diffusion systems, is that their long-time dynamics isdetermined by finitely many parameters, finite number of determining modes, nodes, volume elements and other determining interpolants. In this talk I will show how to explore this finite-dimensional feature of the long-time behavior of infinite-dimensional dissipative systems to design nudging downscaling data assimilation algorithms for weather prediction based on discrete coarse mesh measurements. Moreover, I will also demonstrate uniform in time error estimates of the numerical discretization of these algorithms, which makes reliable upon implementation computationally. Furthermore, I will also present some recent results concerning a statistical version of these algorithms.
Invited by Sebastian Reich