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Parameter recovery for the 2 dimensional Navier-Stokes equations via continuous data assimilation. (English) Zbl 1474.35515

Summary: We study a continuous data assimilation algorithm proposed by A. Azouani et al. [J. Nonlinear Sci. 24, No. 2, 277–304 (2014; Zbl 1291.35168)] (AOT) in the context of an unknown viscosity. We determine the large-time error between the true solution of the 2 dimensional Navier-Stokes equations and the assimilated solution due to discrepancy between an approximate viscosity and the physical viscosity. Additionally, we develop an algorithm that can be run in tandem with the AOT algorithm to recover both the true solution and the true viscosity using only spatially discrete velocity measurements.

MSC:

35Q30 Navier-Stokes equations
35Q35 PDEs in connection with fluid mechanics

Citations:

Zbl 1291.35168

Software:

Dedalus
PDFBibTeX XMLCite
Full Text: DOI

References:

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