## Applied Mathematics Colloquium: Dr. Animikh Biswas

#### UMBC

**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.