On Kato's square root property for the generalized Stokes operator
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.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Journal of Functional Analysis
- Volume
- 290
- Issue
- 10
- Pages
- 111409–111409
- Publication date
- 10 February 2026
- Language
- EN