Applications of the Lieb--Thirring and other bounds for orthonormal systems in mathematical hydrodynamics

Autor:	Ilyin, Alexei, Kostianko, Anna, Zelik, Sergey
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs Mathematics - Spectral Theory 35B40 35B45 35L70
Druh dokumentu:	Working Paper
Popis:	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 Navier--Stokes equations and for a class of $\alpha$-models approximating them. New applications to interpolation inequalities on the 2D torus are also given. Comment: Submitted to a volume on the occasion of Elliott H. Lieb's 90th birthday
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2202.01531 Zobrazit plný text záznamu View this record from Arxiv