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CONTINUOUS DATA ASSIMILATION FOR THE THREE-DIMENSIONAL LERAY-α MODEL WITH STOCHASTICALLY NOISY DATA

  • Bui Kim, My (Department of Mathematics Hanoi Pedagogical University 2) ;
  • Tran Quoc, Tuan (Department of Mathematics Hanoi National University of Education)
  • Received : 2021.12.23
  • Accepted : 2022.04.07
  • Published : 2023.01.31
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Abstract

In this paper we study a nudging continuous data assimilation algorithm for the three-dimensional Leray-α model, where measurement errors are represented by stochastic noise. First, we show that the stochastic data assimilation equations are well-posed. Then we provide explicit conditions on the observation density (resolution) and the relaxation (nudging) parameter which guarantee explicit asymptotic bounds, as the time tends to infinity, on the error between the approximate solution and the actual solution which is corresponding to these measurements, in terms of the variance of the noise in the measurements.

Keywords

Acknowledgement

A part of this paper was completed while the first author visited the Vietnam Institute for Advanced Study in Mathematics (VIASM) in 2021. He would like to thank VIASM for support and hospitality.

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