Downscaling data assimilation algorithm with applications to statistical solutions of the Navier–Stokes equations
- Author(s): Biswas, Animikh;
- Foias, Ciprian;
- Mondaini, Cecilia F;
- Titi, Edriss S
- et al.
Published Web Locationhttps://doi.org/10.1016/j.anihpc.2018.05.004
Based on a previously introduced downscaling data assimilation algorithm, which employs a nudging term to synchronize the coarse mesh spatial scales, we construct a determining map for recovering the full trajectories from their corresponding coarse mesh spatial trajectories, and investigate its properties. This map is then used to develop a downscaling data assimilation scheme for statistical solutions of the two-dimensional Navier-Stokes equations, where the coarse mesh spatial statistics of the system is obtained from discrete spatial measurements. As a corollary, we deduce that statistical solutions for the Navier-Stokes equations are determined by their coarse mesh spatial distributions. Notably, we present our results in the context of the Navier-Stokes equations; however, the tools are general enough to be implemented for other dissipative evolution equations.