Continuous Data Assimilation for the Double-Diffusive Natural Convection

Akbas, Mine; Çıbık, Aytekin

doi:10.48550/arxiv.2008.02224

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2021

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“…Note that another nonlinear approach to nudging was proposed and studied in [51], but using a very different method from that in the present work. In our case, in order to simplify the practical implementation, we consider the following nonlinearnudging system of equations: (1.3b) where we denote, with γ ∈ [0, 1),…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis for the 2D Navier–Stokes Equations with Applications to Continuous Data Assimilation

Carlson

Larios

2021

J Nonlinear Sci

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We study a nonlinear-nudging modification of the Azouani-Olson-Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible Navier-Stokes equations. We give a rigorous proof that the nonlinear-nudging system is globally well-posed, and moreover that its solutions converge to the true solution exponentially fast in time. Furthermore, we also prove that, once the error has decreased below a certain order one threshold, the convergence becomes double-exponentially fast in time, up until a precision determined by the sparsity of the observed data. In addition, we demonstrate the applicability of the analytical and sharpness of the results computationally.

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Section: Introductionmentioning

confidence: 99%