H^∞-calculus for the Stokes operator with Hodge, Navier, and Robin boundary conditions on unbounded domains

2025/04/26 by Kunstmann, Peer Christian
#35Q30 #47A60 #47D06 #76D07 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2504.18895

Abstract

We study the Stokes operator with Hodge, Navier, and Robin boundary conditions on domains Ω⊆ℝ^d that are uniformly C^2,1. Starting with the Hodge Laplacian we etablish a bounded Hörmander functional calculus for the Stokes operator with Hodge boundary conditions. This entails a Hörmander functional calculus and boundedness of the H^∞-calculus in spaces of soleniodal vector fields for the Stokes operator with Hodge boundary conditions. We then establish boundedness of the H^∞-calculus for Stokes operators with Navier type conditions via Robin type perturbations of Hodge boundary conditions. This implies maximal L^p-regularity for these operators and results on fractional domain spaces. Our results cover certain non-Helmholtz domains.

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