Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations

Physica D: Nonlinear Phenomena

Volumn 240, Issue 18, 2011, Pages 1416-1425

  Hayden, Kevin ^a   Olson, Eric ^b   Titi, Edriss S ^c,d  

^a NORTHERN ARIZONA UNIVERSITY   (United States)

^b UNIVERSITY OF NEVADA   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

Assimilation; Chaos; Dynamics; Lorenz; Navier Stokes

Indexed keywords

CHAOS THEORY; DYNAMICAL SYSTEMS; DYNAMICS; SOLUTION MINING; VISCOUS FLOW;

2D NAVIER STOKES EQUATIONS; APPROXIMATE SOLUTION; ASSIMILATION; CONTINUOUS DYNAMICAL SYSTEM; LORENZ; NAVIER STOKES; PARTIAL INFORMATION; TWO-DIMENSIONAL NAVIER-STOKES EQUATIONS;

NAVIER STOKES EQUATIONS;

EID: 79960987018     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2011.04.021     Document Type: Article

References (21)

1. E. Olson, and E.S. Titi Determining modes for continuous data assimilation in 2d turbulence J. Stat. Phys. 113 516 2003 799 840 (Pubitemid 39014969)
2. E. Olson, and E.S. Titi Determining modes and grashoff number for continuous data assimilation in 2d turbulence Theor. Comput. Fluid Dyn. 22 2008 327 339
3. C. Wingard, Removing Bias and Periodic Noise in Measurements of the Lorenz System, Thesis, University of Nevada, Department of Mathematics and Statistics, 2009.
4. C. Foias, and G. Prodi Sur le comportement global des solutions non-stationnaires des eq́uations de NavierStokes en dimension 2 Rend. Semin. Mat. Univ. Padova 39 1967 1 34
5. D.A. Jones, and E.S. Titi On the number of determining nodes for the 2d navierstokes equations J. Math. Anal. Appl. 168 1 1992 72 88
6. D.A. Jones, and E.S. Titi Upper bounds on the number of determining modes, nodes, and volume elements for the NavierStokes equations Indiana Univ. Math. J. 42 3 1993 875 887
7. T. Yang, L. Yang, and C. Yang Impulsive control of lorenz system Physica D 110 12 1997 18 24 (Pubitemid 127701586)
8. X. Wu, J. Lu, C. Wang, and J. Liu Impulsive control and synchronization of the lorenz systems family Chaos Solitons Fractals 31 3 2007 631 638 (Pubitemid 44247633)
9. P.L. houtekamer, and H.L. Mitchell Data assimilation using an ensemble kalman filter technique Mon. Weather Rev. 126 1998 796 811 (Pubitemid 128581567)
10. W. Lee, D. McDougall, A.M. Stuart, Kalman filtering for linear wave equations with model error. arXiv:1101.5096v1.
11. J.A. Hansen, and L.A. Smith Probabilistic noise reduction Tellus A 53 2001 585 598 (Pubitemid 32997329)
12. K. Hayden, Synchronization in the Lorenz System, Masters Thesis, University of Nevada, Department of Mathematics and Statistics, 2007.
13. C. Foias, M.S. Jolly, I. Kukavica, and E.S Titi The lorenz equation as a metaphor for the navierstokes equations Discrete Contin. Dyn. Syst. 7 4 2001 403 429 (Pubitemid 33682305)
14. R. Temam Infinite-dimensional Dynamical Systems in Mechanics and Physics 2nd edition 1997 Springer-Verlag New York
15. P. Constantin, C. Foias, and R. Temam Attractors representing turbulent flows Mem. Amer. Math. Soc. 53 314 1985
16. P. Constantin, and C. Foias NavierStokes equations Chicago Lect. Math. 1988
17. J.C. Robinson Infinite-dimensional dynamical systems: an introduction to dissipative parabolic PDEs and the theory of global attractors Camb. Texts Appl. Math. 2001
18. R. Temam NavierStokes equations and nonlinear functional analysis second edition CBMS-NSF Regional Conference Series in Applied Mathematics vol 66 1995 SIAM
19. O.A. Ladyzhenskaya The Mathematical Theory of Viscous Incompressible Flow 1969 Gordon and Breach Science Publishers Translated from the Russian by R. Silverman and John Chu
20. L. Pecora, and T. Carroll Synchronization in Chaotic systems Phys. Rev. Lett. 64 8 1990 821 824
21. A. Jorba, and M. Zou A software package for the numerical integration of odes by means of high-order taylor methods Experiment. Math. 14 1 2005 99 117 (Pubitemid 41017979)