38 citations · 182 across the 59 of their papers we have counts for
7 papers · 2 filters
Sharp dimension estimates of the attractor of the damped 2D Euler-Bardina equations
Alexei Ilyin, Sergey Zelik
We prove existence of the global attractor of the damped and driven 2D Euler--Bardina equations on the torus and give an explicit two-sided estimate of its dimension that is sharp…
Lieb-Thirring constant on the sphere and on the torus
Alexei Ilyin, Ari Laptev, Sergey Zelik
We prove on the 2D sphere and on the 2D torus the Lieb-Thirring inequalities with improved constants for orthonormal families of scalar and vector functions.
Inertial manifolds via spatial averaging revisited
Anna Kostianko, Xinhua Li, Chunyou Sun +1
The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method suggested by G. Sell and J. M…
Asymptotic regularity and attractors for slightly compressible Brinkman-Forcheimer equations
Varga Kalantarov, Sergey Zelik
Slightly compressible Brinkman-Forchheimer equations in a bounded 3D domain with Dirichlet boundary conditions are considered. These equations model fluids motion in porous media.…
Reaction-diffusion systems with supercritical nonlinearities revisited
Anna Kostianko, Chunyou Sun, Sergey Zelik
We give a comprehensive study of the analytic properties and long-time behavior of solutions of a reaction-diffusion system in a bounded domain in the case where the nonlinearity s…
Validity of the hyperbolic Whitham modulation equations in Sobolev spaces
Thomas J. Bridges, Anna Kostianko, Sergey Zelik
It is proved that modulation in time and space of periodic wave trains, of the defocussing nonlinear Schrödinger equation, can be approximated by solutions of the Whitham modulatio…