A Friedlander type estimate for Stokes operators

2022/03/22 by Clément Denis, Denis, C., A. F. M. ter Elst +1
Mathematics · #35P15 #47A75 #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2203.12070

openalex publication_date 2022/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Ω⊂ ℝ^d be a bounded open connected set with Lipschitz boundary. Let A^N and A^D be the Neumann Stokes operator and Dirichlet Stokes operator on Ω, respectively. Further let λ₁^N ≤ λ₂^N ≤ … and λ₁^D ≤ λ₂^D ≤ … be the eigenvalues of A^N and A^D repeated with multiplicity, respectively. Then λ_n+1^N lt; λ_n^D for all n ∈ ℕ.

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