47 citations · 85 across the 21 of their papers we have counts for
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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…
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…
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…
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…
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…
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…