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

Author

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  • Débora A. F. Albanez

    (Universidade Tecnológica Federal do Paraná)

  • Maicon José Benvenutti

    (Universidade Federal de Santa Catarina)

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.

Suggested Citation

  • Débora A. F. Albanez & Maicon José Benvenutti, 2024. "Parameter analysis in continuous data assimilation for three-dimensional Brinkman–Forchheimer-extended Darcy model," Partial Differential Equations and Applications, Springer, vol. 5(4), pages 1-32, August.
    • Handle: RePEc:spr:pardea:v:5:y:2024:i:4:d:10.1007_s42985-024-00288-w
    DOI: 10.1007/s42985-024-00288-w
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    References listed on IDEAS

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    1. Weihua Wang & Guopeng Zhou, 2015. "Remarks on the Regularity Criterion of the Navier-Stokes Equations with Nonlinear Damping," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-5, July.
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