Continuous Data Assimilation for the Three Dimensional Navier-Stokes\n Equations

2020/03/02 by Animikh Biswas, Biswas, Animikh, Randy Price +1 · 4 citations
Engineering · Mathematics · #35Q30 #35Q35 #76B75 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2003.01329

openalex publication_date 2020/03/02 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we provide conditions, \based solely on the observed\ndata, for the global well-posedness, regularity and convergence of the\nAzouni-Olson-Titi data assimilation algorithm (AOT algorithm) for a Leray-Hopf\nweak solutions of the three dimensional Navier-Stokes equations (3D NSE). The\naforementioned conditions on the observations, which in this case comprise\neither of \modal or \volume element observations, are automatically\nsatisfied for solutions that are globally regular and are uniformly bounded in\nthe H¹-norm. However, neither regularity nor uniqueness is necessary for the\nefficacy of the AOT algorithm. To the best of our knowledge, this is the first\nsuch rigorous analysis of the AOT data assimilation algorithm for the 3D NSE.\n

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• Data Assimilation in Large Eddy Simulation: Addressing Model-Observation Mismatch from Navier-Stokes Data

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