期刊
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
卷 36, 期 2, 页码 295-326出版社
ELSEVIER
DOI: 10.1016/j.anihpc.2018.05.004
关键词
Data assimilation; Downscaling; Nudging; Navier-Stokes equations; Determining form; Vishik-Fursikov statistical solutions
资金
- NSF [DMS 1517027, DMS 1516866]
- ONR [N00014-15-1-2333]
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. (C) 2018 Elsevier Masson SAS. All rights reserved.
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