3 citations · 7 across the 11 of their papers we have counts for
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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…
Determining functionals and finite-dimensional reduction for dissipative PDEs revisited
Varga Kalantarov, Anna Kostianko, Sergey Zelik
We study the properties of linear and non-linear determining functionals for dissipative dynamical systems generated by PDEs. The main attention is payed to the lower bounds for th…
Dimension estimates for the attractor of the regularized damped Euler equations on the sphere
Alexei Ilyin, Anna Kostianko, Sergey Zelik
We prove existence of the global attractor of the damped and driven Euler--Bardina equations on the 2D sphere and on arbitrary domains on the sphere and give explicit estimates of…
Inertial manifolds for 3D complex Ginzburg-Landau equations with periodic boundary conditions
Anna Kostianko, Chunyou Sun, Sergey Zelik
We prove the existence of an Inertial Manifold for 3D complex Ginzburg-Landau equation with periodic boundary conditions as well as for more general cross-diffusion system assuming…
Sharp upper and lower bounds of the attractor dimension for 3D damped Euler-Bardina equations
Alexei Ilyin, Anna Kostianko, Sergey Zelik
The dependence of the fractal dimension of global attractors for the damped 3D Euler--Bardina equations on the regularization parameter and Ekman damping coefficient is…
Smooth extensions for inertial manifolds of semilinear parabolic equations
Anna Kostianko, Sergey Zelik
The paper is devoted to a comprehensive study of smoothness of inertial manifolds for abstract semilinear parabolic problems. It is well known that in general we cannot expect more…