38 citations · 182 across the 59 of their papers we have counts for
6 papers · 2 filters
The non-autonomous Navier-Stokes-Brinkman-Forchheimer equation with Dirichlet boundary conditions: dissipativity, regularity, and attractors
Dominic Stone, Sergey Zelik
We give a comprehensive study of the 3D Navier-Stokes-Brinkman-Forchheimer equations in a bounded domain endowed with the Dirichlet boundary conditions and non-autonomous external…
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…
Non-concentration phenomenon for one dimensional reaction-diffusion systems with mass dissipation
Juan Yang, Anna Kostianko, Chunyou Sun +2
Reaction-diffusion systems with mass dissipation are known to possess blow-up solutions in high dimensions when the nonlinearities have super quadratic growth rates. In dimension o…
On a class of interpolation inequalities on the 2D sphere
Alexei Ilyin, Sergey Zelik
We prove estimates for the -norms of systems of functions and divergence free vector functions that are orthonormal in the Sobolev space on the 2D sphere. As a corollary…
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…