Continuous data assimilation for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field
J. Korean Math. Soc. 2021 Vol. 58, No. 1, 1-28
https://doi.org/10.4134/JKMS.j190356
Published online September 28, 2020
Printed January 1, 2021
Cung The Anh, Bui Huy Bach
Hanoi National University of Education; Hanoi National University of Education
Abstract : We study a continuous data assimilation algorithm for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field. Under suitable conditions on the relaxation (nudging) parameter and the spatial mesh resolution, we obtain an asymptotic in time estimate of the difference between the approximating solution and the unknown reference solution corresponding to the measurements, in an appropriate norm, which shows exponential convergence up to zero.
Keywords : 3D simplified Bardina model, continuous data assimilation, interpolant, coarse measurements of velocity, nudging
MSC numbers : 35Q30, 93C20, 37C50, 76B75, 34D06
Supported by : This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2018.303.
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