Applied Mathematics Colloquium: Dr. Animikh Biswas
Title: A Continuous Data Assimilation Algorithm with Applications to Statistical Solutions
Speaker: Animikh Biswas, UMBC
Abstract: Based on a down-scaling data assimilation algorithm, which employs a nudging term on the coarse scales, we construct a determining map of coarse scale trajectories and investigate its properties. This map is then used to develop a data assimilation scheme for statistical solutions of the two-dimensional Navier-Stokes equations, where the coarse scale statistics of the system is obtained from measurements. As a corollary, we deduce that the statistical solutions for the Navier-Stokes equations are determined by their coarse mesh spatial distributions. This is based on a joint work with C. Foias, C. Mondaini and E. S. Titi.