Zusammenfassung
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 ...
Zusammenfassung
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.
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