Continuous data assimilation for the three-dimensional simplified Bardina model utilizing measurements of only two components of the velocity field
J. Korean Math. Soc.
Published online September 28, 2020
Cung The Anh and Bui Huy Bach
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.
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