We analyze continuous data assimilation by nudging for the 3D Ladyzhenskaya equations. The analysis provides conditions on the spatial resolution of the observed data that guarantee synchronization to the reference solution associated with the observed, spatially coarse data. This synchronization holds even though it is not known whether the reference solution, with initial data in $L^2$, is unique; a particular reference solution is determined by the observed, coarse data. The efficacy of the algorithm in both 2D and 3D is demonstrated by numerical computations.
Auto-differentiable data assimilation: Co-learning of states, dynamics, and filtering algorithms
School of Mechanical Engineering, Purdue University（普渡大学机械工程学院）；Department of Statistics, The University of Chicago（芝加哥大学统计学系）；Department of Computer Science, The University of Chicago（芝加哥大学计算机科学系）；NSF-Simons National Institute for Theory and Mathematics in Biology, Chicago, IL（国家理论与生物数学研究所）
Cheap2Rich: A Multi-Fidelity Framework for Data Assimilation and System Identification of Multiscale Physics -- Rotating Detonation Engines
Department of Electrical；Computer Engineering, University of Washington, Seattle, USA；Department of Applied Mathematics, University of Washington, Seattle, USA；University of Michigan, Advanced Propulsion Concepts Lab, Ann Arbor, USA；Department of Mathematics, Swiss Federal Institute of Technology Zurich, Zurich, Switzerland
