3 citations · 7 across the 7 of their papers we have counts for
12 papers
Entropy estimates for uniform attractors of dissipative PDEs with non translation-compact external forces
Yangmin Xiong, Anna Kostianko, Chunyou Sun +1
We study the Kolmogorov's entropy of uniform attractors for non-autonomous dissipative PDEs. The main attention is payed to the case where the external forces are not translation-c…
Applications of the Lieb--Thirring and other bounds for orthonormal systems in mathematical hydrodynamics
Alexei Ilyin, Anna Kostianko, Sergey Zelik
We discuss the estimates for the -norms of systems of functions that are orthonormal in and , respectively, and their essential role in deriving good or even optima…
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…
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…