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Discrete data assimilation for the three-dimensional Navier–Stokes-$\alpha $ model

Volume 122 / 2019

Cung The Anh, Bui Huy Bach, Vu Manh Toi Annales Polonici Mathematici 122 (2019), 201-219 MSC: 35Q35, 37C50, 76B75, 93C20. DOI: 10.4064/ap180605-3-4 Published online: 2 September 2019

Abstract

We study the data assimilation for the three-dimensional Navier–Stokes-$\alpha $ model when the measurements are obtained discretely in time and may be contaminated by systematic errors. Under suitable conditions on the relaxation (nudging) parameter, the spatial mesh resolution, and the time step between successive measurements, 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. In the particular case of error-free measurements, we have exponential convergence of the approximating solution toward the reference solution.

Authors

  • Cung The AnhDepartment of Mathematics
    Hanoi National University of Education
    136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
    e-mail
  • Bui Huy BachDepartment of Mathematics
    Hanoi National University of Education
    136 Xuan Thuy, Cau Giay, Hanoi, Vietnam
    e-mail
  • Vu Manh ToiFaculty of Computer Science and Engineering
    Thuyloi University
    175 Tay Son, Dong Da, Hanoi, Vietnam
    e-mail

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