On the spectrum of the Stokes operator

TL;DR

This paper establishes lower bounds for the eigenvalues of the Stokes operator, with implications for understanding the behavior of solutions to the Navier--Stokes equations.

Contribution

It provides Li--Yau-type lower bounds for the Stokes operator eigenvalues, a novel result in spectral analysis relevant to fluid dynamics.

Findings

Derived lower bounds for Stokes eigenvalues

Applied bounds to Navier--Stokes attractors

Enhanced understanding of fluid flow spectral properties

Abstract

We prove Li--Yau-type lower bounds for the eigenvalues of the Stokes operator and give applications to the attractors of the Navier--Stokes equations.