Refined bounds for the eigenvalues of the Stokes operator

Zhengchao Ji and Türkay Yolcu

Vol. 343 (2026), No. 1, 119–137

DOI: 10.2140/pjm.2026.343.119

Abstract

We analyze bounds for the sums of eigenvalues of the Stokes operator restricted to a bounded domain $\mathrm{\Omega }\subset {ℝ}^d$ with $d\ge 2$. We improve upon existing lower bound estimates due to Ilyin as well as those by the second author and S. Yıldırım Yolcu, while preserving sharpness in the sense of Weyl asymptotics.

Keywords

Stokes operator, Berezin–Li–Yau inequality, eigenvalue, inequality, Weyl asymptotics

Mathematical Subject Classification

Primary: 35P15

Secondary: 35P30

Milestones

Received: 12 July 2025

Revised: 11 February 2026

Accepted: 25 March 2026

Published: 29 April 2026