Work

On Kato's square root property for the generalized Stokes operator

Year: 2026

Type: article

Abstract: We establish the Kato square root property for the generalized Stokes operator on R d with bounded measurable coefficients. More precisely, we identify the domain of the square root of A u ≔ − div ( μ ∇ u ) + ∇ ϕ , div ( u ) = 0 , with the space of divergence-free H 1 -vector fields and further prove the estimate ‖ A 1 / 2 u ‖ L 2 ≃ ‖ ∇ u ‖ L 2 . As an application we show that A 1 / 2 depends holomorphically on the coefficients μ . Besides the boundedness and measurability as well as an ellipticity condition on μ , there are no requirements on the coefficients.

Source: Journal of Functional Analysis

DOI: 10.1016/j.jfa.2026.111409

Authors: Luca Haardt, Patrick Tolksdorf

Institution: Karlsruhe Institute of Technology

Language: English

Topic: Advanced Harmonic Analysis Research

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,250

Funder: Studienstiftung des Deutschen Volkes