Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

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J. Korean Math. Soc. 2021; 58(1): 1-28

Online first article September 28, 2020      Printed January 1, 2021

https://doi.org/10.4134/JKMS.j190356

Copyright © The Korean Mathematical Society.

Continuous data assimilation for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field

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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