Continuous data assimilation for the 3D Ladyzhenskaya model: analysis and computations. (December 2022)

• Record Type: Journal Article
• Authors: Cao, Yu; Giorgini, Andrea; Jolly, Michael; Pakzad, Ali
• Is Part Of: Nonlinear analysis. Volume 68(2022)
• Publication Date: 2022-12
• Subjects: Data assimilation -- Ladyzhenskaya model -- Non-Newtonian fluids -- Large eddy simulation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103659
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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; any 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.