Downscaling data assimilation algorithm with applications to statistical solutions of the Navier-Stokes equations

DOI10.1016/j.anihpc.2018.05.004zbMath1420.35181arXiv1711.04067OpenAlexW2964178943MaRDI QIDQ1719938

Edriss S. Titi, Ciprian Foias, Animikh Biswas, Cecilia F. Mondaini

Publication date: 12 February 2019

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.04067

zbMATH Keywords

Navier-Stokes equationsdata assimilationdownscalingnudgingdetermining mapVishik-Fursikov statistical solutions

Mathematics Subject Classification ID

Feedback control (93B52) Theoretical approximation of solutions to ordinary differential equations (34A45) Navier-Stokes equations (35Q30) Inverse problems involving ordinary differential equations (34A55) Inertial manifolds (35B42) Statistical solutions of Navier-Stokes and related equations (76D06)

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Cites Work

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• Sampling, feasibility, and priors in data assimilation
• Abstract framework for the theory of statistical solutions
• Abridged continuous data assimilation for the 2D Navier-Stokes equations utilizing measurements of only one component of the velocity field
• Feedback control of nonlinear dissipative systems by finite determining parameters -- a reaction-diffusion paradigm
• Higher-order synchronization for a data assimilation algorithm for the 2D Navier-Stokes equations
• Determining form and data assimilation algorithm for weakly damped and driven Korteweg-de Vries equation -- Fourier modes case
• Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equations
• Diffusive back and forth nudging algorithm for data assimilation
• Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations
• Inertial manifolds for nonlinear evolutionary equations
• Integral manifolds and inertial manifolds for dissipative partial differential equations
• Sur les solutions statistiques des équations de Navier-Stokes
• Infinite-dimensional dynamical systems in mechanics and physics.
• Assimilation of nearly turbulent Rayleigh-Bénard flow through vorticity or local circulation measurements: a computational study
• Finite determining parameters feedback control for distributed nonlinear dissipative systems -- a computational study
• One-dimensional parametric determining form for the two-dimensional Navier-Stokes equations
• Downscaling the 2D Bénard convection equations using continuous data assimilation
• Statistical study of Navier-Stokes equations. I
• Statistical study of Navier-Stokes equations. II
• Accuracy and stability of filters for dissipative PDEs
• A determining form for the damped driven nonlinear Schrödinger equation -- Fourier modes case
• A note on statistical solutions of the three-dimensional Navier-Stokes equations: the time-dependent case
• A determining form for the subcritical surface quasi-geostrophic equation
• Continuous data assimilation for the 2D Bénard convection through velocity measurements alone
• On the Charney conjecture of data assimilation employing temperature measurements alone: the paradigm of 3D planetary geostrophic model
• Continuous data assimilation using general interpolant observables
• Properties of time-dependent statistical solutions of the three-dimensional Navier-Stokes equations
• Sur le comportement global des solutions non-stationnaires des équations de Navier-Stokes en dimension 2
• Continuous data assimilation for the three-dimensional Brinkman–Forchheimer-extended Darcy model
• Continuous data assimilation for the three-dimensional Navier–Stokes-α model
• Accuracy and stability of the continuous-time 3DVAR filter for the Navier–Stokes equation
• A determining form for the two-dimensional Navier-Stokes equations: The Fourier modes case
• A unified approach to determining forms for the 2D Navier-Stokes equations -- the general interpolants case
• Determining nodes, finite difference schemes and inertial manifolds
• Determination of the Solutions of the Navier-Stokes Equations by a Set of Nodal Values
• On a criterion for locating stable stationary solutions to the Navier-Stokes equations
• Mathematical Problems of Statistical Hydromechanics
• Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems
• Uniform-in-Time Error Estimates for the Postprocessing Galerkin Method Applied to a Data Assimilation Algorithm
• Real Analysis and Probability
• Probabilistic Forecasting and Bayesian Data Assimilation
• Continuous data assimilation with stochastically noisy data
• Data Assimilation
• Data Assimilation
• A Computational Study of a Data Assimilation Algorithm for the Two-dimensional Navier-Stokes Equations
• Filtering Complex Turbulent Systems
• A Discrete Data Assimilation Scheme for the Solutions of the Two-Dimensional Navier--Stokes Equations and Their Statistics
• Observing the state of non-linear dynamic systems
• Time analyticity with higher norm estimates for the 2D Navier-Stokes equations
• Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates
• A dynamical control view on synchronization
• Data assimilation algorithm for 3D Bénard convection in porous media employing only temperature measurements

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