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Approximate continuous data assimilation of the 2D Navier-Stokes equations via the Voigt-regularization with observable data.
- Source :
- Evolution Equations & Control Theory; Sep2020, Vol. 9 Issue 3, p733-751, 19p
- Publication Year :
- 2020
-
Abstract
- We propose a data assimilation algorithm for the 2D Navier-Stokes equations, based on the Azouani, Olson, and Titi (AOT) algorithm, but applied to the 2D Navier-Stokes-Voigt equations. Adapting the AOT algorithm to regularized versions of Navier-Stokes has been done before, but the innovation of this work is to drive the assimilation equation with observational data, rather than data from a regularized system. We first prove that this new system is globally well-posed. Moreover, we prove that for any admissible initial data, the L<superscript>2</superscript> and H<superscript>1</superscript> norms of error are bounded by a constant times a power of the Voigt-regularization parameter α > 0, plus a term which decays exponentially fast in time. In particular, the large-time error goes to zero algebraically as α goes to zero. Assuming more smoothness on the initial data and forcing, we also prove similar results for the H<superscript>2</superscript> norm. [ABSTRACT FROM AUTHOR]
- Subjects :
- NAVIER-Stokes equations
ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 21632472
- Volume :
- 9
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Evolution Equations & Control Theory
- Publication Type :
- Academic Journal
- Accession number :
- 144613882
- Full Text :
- https://doi.org/10.3934/eect.2020031