Lieb-Thirring inequalities on the torus

TL;DR

This paper proves Lieb-Thirring inequalities on the d-dimensional torus with arbitrary periods, providing bounds for negative eigenvalues that are independent of period ratios, with applications to damped Navier-Stokes attractors.

Contribution

It establishes Lieb-Thirring inequalities on the torus with period-independent constants for functions with zero average, extending previous results to more general periodic settings.

Findings

Lieb-Thirring inequalities hold on the torus with arbitrary periods.

Constants in inequalities are independent of period ratios.

Applications to attractors in damped Navier-Stokes systems.

Abstract

We consider the Lieb-Thirring inequalities on the d-dimensional torus with arbitrary periods. In the space of functions with zero average with respect to the shortest coordinate we prove the Lieb-Thirring inequalities for the $\gamma$-moments of the negative eigenvalues with constants independent of ratio of the periods. Applications to the attractors of the damped Navier-Stokes system are given.