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

  • Pascal Hobus

    Heinrich-Heine-Universität Düsseldorf, Germany
  • Jürgen Saal

    Heinrich-Heine-Universität Düsseldorf, Germany
Triebel–Lizorkin–Lorentz Spaces and the Navier–Stokes Equations cover
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Abstract

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 , to have property , 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 -calculus. This is finally applied to construct a unique maximal strong solution for the Navier–Stokes equations on corresponding Triebel–Lizorkin–Lorentz ground spaces.

Cite this article

Pascal Hobus, Jürgen Saal, Triebel–Lizorkin–Lorentz Spaces and the Navier–Stokes Equations. Z. Anal. Anwend. 38 (2019), no. 1, pp. 41–72

DOI 10.4171/ZAA/1627