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

2022/02/03 by Alexei Ilyin, Ilyin, Alexei, Anna Kostianko +3 · 1 citation
Engineering · Mathematics · #35B40 #35B45 #35L70 #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Spectral Theory (math.SP) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2202.01531

openalex publication_date 2022/02/03 · openalex created_date 2022/04/03 · openalex updated_date 2026/08/01

Abstract

We discuss the estimates for the L^p-norms of systems of functions that are orthonormal in L² and H¹, 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 α-models approximating them. New applications to interpolation inequalities on the 2D torus are also given.

Cited by

• Attractor of the limiting Navier--Stokes--Voigt system in \mathbb R⁴

Related

• Lieb--Thirring inequalities on the sphere
• On the role of L³ and H^(1)/(2) norms in hydrodynamics
• Time analyticity with higher norm estimates for the 2D Navier-Stokes equations
• On a class of interpolation inequalities on the 2D sphere
• Lieb-Thirring inequalities and other functional inequalities for orthonormal systems