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Determining nodes, finite difference schemes and inertial manifolds
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Determination of the solutions of the Navier-Stokes equations by finite volume elements
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Sur le comportement global des solutions non stationnaires des équations de Navier-Stokes en dimension two
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Determination of the solutions of the Navier-Stokes equations by a set of nodal values
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Foias, C.1
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Asymptotic analysis of the Navier-Stokes equations
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C. Foias, O. P. Manley, R. Temam, and Y. Treve, "Asymptotic analysis of the Navier-Stokes equations," Physica D 9, 157-188 (1983).
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On the number of determining nodes for the 2D Navier-Stokes equations
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D. A. Jones and E. S. Titi, "On the number of determining nodes for the 2D Navier-Stokes equations," J. Math. Anal. Appl. 168, 72-88 (1992).
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Upper bounds on the number of determining modes, nodes, and volume elements for the Navier-Stokes equations
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D. A. Jones and E. S. Titi, "Upper bounds on the number of determining modes, nodes, and volume elements for the Navier-Stokes equations," Indiana Univ. Math. J. 42, 875-887 (1993).
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Degrés de liberté déterminants pour équations nonlinéaires dissipatives
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B. Cockburn, D. Jones, and E. S. Titi, "Degrés de liberté déterminants pour équations nonlinéaires dissipatives," Compt. Rendus Acad. Sci. Paris Sér. I 321, 563-568 (1995).
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Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems
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B. Cockburn, D. Jones, and E. S. Titi, "Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems," Math. Comp. (in press).
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Math. Comp.
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Determining modes and fractal dimension of turbulent flows
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P. Constantin, C. Foias, O. P. Manley, and R. Temam, "Determining modes and fractal dimension of turbulent flows," J. Fluid Mech. 150, 427-440 (1985).
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Length scales in solutions of the Navier-Stokes equations
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M. Bartuccelli, C. R. Doering, J. D. Gibbon, and S. J. A. Malham, "Length scales in solutions of the Navier-Stokes equations," Nonlinearity 6, 549-568 (1993).
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Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations
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C. R. Doering and E. S. Titi, "Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations," Phys. Fluids 7, 1384-1390 (1995).
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Attractor dimension and small length scale estimates for the 3-d Navier-Stokes equations
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J. D. Gibbon and E. S. Titi, "Attractor dimension and small length scale estimates for the 3-d Navier-Stokes equations," Nonlinearity (in press).
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On the smallest scale for the incompressible Navier-Stokes equations
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W. D. Henshaw, H. O. Kreiss, and L. G. Reyna, "On the smallest scale for the incompressible Navier-Stokes equations," Arch. Rat. Mech. Anal. 112, 21-44 (1990).
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Local structure of turbulence in an incompressible fluid at very high Reynolds numbers
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A. Kolmogorov, "Local structure of turbulence in an incompressible fluid at very high Reynolds numbers," Dokl. Akad. Nauk. SSSR 30, 299-303 (1941).
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