Parameter analysis in continuous data assimilation for three-dimensional Brinkman–Forchheimer-extended Darcy model

Débora A. F. Albanez () and Maicon José Benvenutti ()
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Débora A. F. Albanez: Universidade Tecnológica Federal do Paraná
Maicon José Benvenutti: Universidade Federal de Santa Catarina

Partial Differential Equations and Applications, 2024, vol. 5, issue 4, 1-32

Abstract: Abstract In this paper, we study analytically the long-time behavior of three-dimensional Brinkman–Forchheimer-extended Darcy model, in the context that the parameters related to the damping nonlinear term are unknown. This work is inspired by the approach firstly introduced for two-dimensional Navier–Stokes equations by Carlson, Hudson and Larios. We show estimates in $$L^2$$ L 2 and $$H^1$$ H 1 for large-time error between the true solution and the assimilated solution, which is constructed with the unknown damping parameters and observational measurements obtained continuously in time from a continuous data assimilation technique proposed by Azouani, Olson and Titi.

Keywords: Parameter analysis; Navier–Stokes equations; Damping; Continuous data assimilation; Synchronization; 93C20; 76D05; 37C55; 35Q35; 35Q30; 34D06 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42985-024-00288-w

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