The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (560 KB) | Metadata | Table of Contents | ZAA summary
Volume 38, Issue 1, 2019, pp. 41–72
DOI: 10.4171/ZAA/1627

Published online: 2019-01-07

Triebel–Lizorkin–Lorentz Spaces and the Navier–Stokes Equations

Pascal Hobus[1] and Jürgen Saal[2]

(1) Heinrich-Heine-Universität Düsseldorf, Germany
(2) Heinrich-Heine-Universität Düsseldorf, Germany

We derive basic properties of Triebel–Lizorkin–Lorentz spaces important in the treatment of PDE. For instance, we prove Triebel–Lizorkin–Lorentz spaces to be of class $\mathcal {HT}$, to have property $(\alpha)$, and to admit a multiplier result of Mikhlin type. By utilizing these properties we prove the Laplace and the Stokes operator to admit a bounded $H^\infty$-calculus. This is finally applied to construct a unique maximal strong solution for the Navier–Stokes equations on corresponding Triebel–Lizorkin–Lorentz ground spaces.

Keywords: Triebel–Lizorkin–Lorentz spaces, Navier–Stokes equations, local wellposedness

Hobus Pascal, Saal Jürgen: Triebel–Lizorkin–Lorentz Spaces and the Navier–Stokes Equations. Z. Anal. Anwend. 38 (2019), 41-72. doi: 10.4171/ZAA/1627