Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Ilyin, Alexei"'
Autor:
Ilyin, Alexei, Laptev, Ari
In this paper we prove Lieb--Thirring inequalities for magnetic Schr\"odinger operators on the torus, where the constants in the inequalities depend on the magnetic flux.
Externí odkaz:
http://arxiv.org/abs/2305.20023
In this short note we prove Lieb--Thirring inequalities on manifolds with negative constant curvature. The discrete spectrum appears below the continuous spectrum $(d-1)^2/4, \infty)$, where $d$ is the dimension of the hyperbolic space. As an applica
Externí odkaz:
http://arxiv.org/abs/2305.10189
Autor:
Ilyin, Alexei, Zelik, Sergey
We prove estimates for the $L^p$-norms of systems of functions and divergence free vector functions that are orthonormal in the Sobolev space $H^1$ on the 2D sphere. As a corollary, order sharp constants in the embedding $H^1\hookrightarrow L^q$, $q<
Externí odkaz:
http://arxiv.org/abs/2204.12414
We discuss the estimates for the $L^p$-norms of systems of functions that are orthonormal in $L^2$ and $H^1$, respectively, and their essential role in deriving good or even optimal bounds for the dimension of global attractors for the classical Navi
Externí odkaz:
http://arxiv.org/abs/2202.01531
We study the global attractors for the damped 3D Euler--Bardina equations with the regularization parameter $\alpha>0$ and Ekman damping coefficient $\gamma>0$ endowed with periodic boundary conditions as well as their damped Euler limit $\alpha\to0$
Externí odkaz:
http://arxiv.org/abs/2112.13691
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 its fractal dimension in terms of the physical parameters.
Externí odkaz:
http://arxiv.org/abs/2107.10779
The dependence of the fractal dimension of global attractors for the damped 3D Euler--Bardina equations on the regularization parameter $\alpha>0$ and Ekman damping coefficient $\gamma>0$ is studied. We present explicit upper bounds for this dimensio
Externí odkaz:
http://arxiv.org/abs/2106.09077
Autor:
Ilyin, Alexei, Zelik, Sergey
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 as $\alpha\to0^+$.
Externí odkaz:
http://arxiv.org/abs/2011.00607
We prove on the 2D sphere and on the 2D torus the Lieb-Thirring inequalities with improved constants for orthonormal families of scalar and vector functions.
Externí odkaz:
http://arxiv.org/abs/2009.00527
Autor:
Ilyin, Alexei, Laptev, Ari
We prove on the sphere $\mathbb{S}^2$ the Lieb--Thirring inequalities for orthonormal families of scalar and vector functions both on the whole sphere and on proper domains on $\mathbb{S}^2$. By way of applications we obtain an explicit estimate for
Externí odkaz:
http://arxiv.org/abs/1804.09632