Pruess, Jan and Wilke, Mathias (2018) On Critical Spaces for the Navier-Stokes Equations. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 20 (2). pp. 733-755. ISSN 1422-6928, 1422-6952
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The abstract theory of critical spaces developed in pruss and Wilke (J Evol Equ, 2017. doi:10.1007/ s00028-017-0382-6), Pruss et al. (Critical spaces for quasilinear parabolic evolution equations and applications, 2017) is applied to the Navier-Stokes equations in bounded domains with Navier boundary conditions as well as no-slip conditions. Our approach unifies, simplifies and extends existing work in the L-p-L-q setting, considerably. As an essential step, it is shown that the strong and weak Stokes operators with Navier conditions admit an H-infinity-calculus with H-infinity-angle 0, and the real and complex interpolation spaces of these operators are identified.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PARABOLIC EVOLUTION-EQUATIONS; BOUNDARY-CONDITIONS; MAXIMAL REGULARITY; WELL-POSEDNESS; INITIAL-VALUE; SYSTEM; Navier-Stokes equations; Navier boundary conditions; perfect-slip boundary conditions; critical spaces; functional calculus; weak and strong Stokes operator |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 17 Feb 2020 14:00 |
| Last Modified: | 17 Feb 2020 14:00 |
| URI: | https://pred.uni-regensburg.de/id/eprint/14501 |
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