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Attractors and their dimensions for the 3D Fractional Navier--Stokes--Voigt Equations
Alexei Ilyin, Varga Kalantarov, Sergey Zelik
We study the dimensions of the attractors for the fractional Navier--Stokes--Voigt equations. These equations, which include a fractional order of the Stokes operator applied to th…
Attractor of the limiting Navier--Stokes--Voigt system in
Alexei Ilyin, Varga Kalantarov, Sergey Zelik
The Navier--Stokes--Voigt system in the whole four-dimensional space is considered. Although we do not know any physical reasons to consider this system in space dimension four, th…
Multi-vortices and lower bounds on the attractor dimensions for 2D Navier--Stokes equations
Anna Kostianko, Alexei Ilyin, Dominic Stone +1
We present a principally new method for obtaining the lower bounds for the attractors dimensions of the equations related with hydrodynamics, which is not based on the Kolmogorov f…
Attractors for the Navier--Stokes--Voight equations and their dimension
Alexei Ilyin, Sergey Zelik
The Voight regularization of the Navier--Stokes system is studied in a bounded domain and on the torus. In the 3D case we obtain new explicit bounds for the attractor dimension imp…