1 citations · 1 across the 5 of their papers we have counts for
5 papers
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 for semigroups with multi-dimensional time and PDEs in unbounded domains
Anna Kostianko, Sergey Zelik
We develop the attractors theory for the semigroups with multidimensional time belonging to some closed cone in an Euclidean space and apply the obtained general results to partial…
Trajectory attractors for 3D damped Euler equations and their approximation
Alexei Ilyin, Anna Kostianko, Sergey Zelik
We study the global attractors for the damped 3D Euler--Bardina equations with the regularization parameter and Ekman damping coefficient endowed with periodic boundary…
Inertial Manifolds for the Hyperbolic Relaxation of Semilinear Parabolic Equations
V. Chepyzhov, A. Kostianko, S. Zelik
The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing…
Inertial Manifolds for the 3D Cahn-Hilliard Equations with Periodic Boundary Conditions
Anna Kostianko, Sergey Zelik
The existence of an inertial manifold for the 3D Cahn-Hilliard equation with periodic boundary conditions is verified using the proper extension of the so-called spatial averaging…