On the dimension of the attractors in two-dimensional turbulence
References (26)
- et al.
Nonlinear Schrödinger evolution equations
Nonlinear Analysis Theory, Methods and Applications
(1980) - et al.
Asymptotic analysis of the Navier-Stokes equations
Physica
(1983) An Lp bound for the Riesz and Bessel potentials of orthonormal functions
J. Funct. Analysis
(1983)Computation of the energy spectrum in homogeneous, two dimensional turbulence
Phys. Fluids
(1969)- et al.
Les attracteurs des équations d'évolution et les estimations de leurs dimensions
Usp. Math. Nauk
(1983) Collective L∞ estimates for families of functions with orthonormal derivatives
Indiana University Math. J.
(1987)- et al.
Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractors for 2D Navier-Stokes equations
Comm. Pure Appl. Math.
(1985) - et al.
Attractors representing turbulent flows
Memoirs of A.M.S.
(January, 1985) - et al.
Determining modes and fractal dimensions of turbulent flows
J. Fluid Mech.
(1985) - P. Constantin, C. Foias, B. Nicolaenko and R. Temam, Integral and inertial manifolds for dissipative PDE's,...
Some analytic and geometric properties of the solutions of the Navier-Stokes equations
J. Math. Pures Appl.
(1979)
Inertial ranges in two-dimensional turbulence
Phys. Fluids
(1967)
Cited by (180)
Sharp upper and lower bounds of the attractor dimension for 3D damped Euler–Bardina equations
2022, Physica D: Nonlinear PhenomenaCitation Excerpt :Again, to the best of our knowledge, this is the first optimal two-sided estimate for the attractor dimension in a 3D hydrodynamical problem. In this connection we recall the celebrated upper bound in [27] for the attractor dimension of the classical Navier–Stokes system on the 2D torus, which is still logarithmically larger than the corresponding lower bound in [26]. On the other hand, adding to the system an arbitrary fixed damping makes it possible to obtain the estimate for the attractor dimension that is optimal in the vanishing viscosity limit [25].
On attractor's dimensions of the modified Leray-alpha equation
2023, Asymptotic Analysis
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