1 citations · 1 across the 6 of their papers we have counts for
7 papers
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…
Sharp bounds on the attractor dimensions for damped wave equations
A. A. Ilyin, A. G. Kostianko, S. V. Zelik
We give the explicit estimates of order (with logarithmic correction in the 1D case) for the fractal dimension of the attractor of the damped hyperbolic equation (or syste…
Restoring the Navier--Stokes dynamics by determining functionals depending on pressure
A. Ilyin, V. Kalantarov, A. Kostianko +1
For 2D Navier--Stokes equations in a bounded smooth domain, we construct a system of determining functionals which consists of linear continuous functionals which depend on pre…
Attractors. Then and now
Sergey Zelik
This survey is dedicated to the 100th anniversary of Mark Iosifovich Vishik and is based on a number of mini-courses taught by the author at University of Surrey (UK) and Lanzhou U…