2017/11/10 by Animikh Biswas, Ciprian Foiaş, Biswas, Animikh +5 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1711.04067
openalex publication_date 2017/11/10 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Based on a previously introduced downscaling data assimilation algorithm,\nwhich employs a nudging term to synchronize the coarse mesh spatial scales, we\nconstruct a determining map for recovering the full trajectories from their\ncorresponding coarse mesh spatial trajectories, and investigate its properties.\nThis map is then used to develop a downscaling data assimilation scheme for\nstatistical solutions of the two-dimensional Navier-Stokes equations, where the\ncoarse mesh spatial statistics of the system is obtained from discrete spatial\nmeasurements. As a corollary, we deduce that statistical solutions for the\nNavier-Stokes equations are determined by their coarse mesh spatial\ndistributions. Notably, we present our results in the context of the\nNavier-Stokes equations; however, the tools are general enough to be\nimplemented for other dissipative evolution equations.\n