47 citations · 85 across the 21 of their papers we have counts for
25 papers
Magnetic Lieb--Thirring inequalities on the torus
Alexei Ilyin, Ari Laptev
In this paper we prove Lieb--Thirring inequalities for magnetic Schrödinger operators on the torus, where the constants in the inequalities depend on the magnetic flux.
Lieb--Thirring inequalities on manifolds with constant negative curvature
Alexei Ilyin, Ari Laptev, Timon Weinmann
In this short note we prove Lieb--Thirring inequalities on manifolds with negative constant curvature. The discrete spectrum appears below the continuous spectrum $(d-1)^2/4, \inft…
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…