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Addendum to the paper “On quasilinear parabolic evolution equations in weighted \(L_p\)-spaces II”

Abstract

This note is devoted to a small, but essential, extension of Theorem 2.1 of our recent paper (LeCrone et al. J Evolut Equ 14:509–533 2014). The improvement is explained in “The improvement” section and proved in “Proof of the main result” section. The importance of the extension is demonstrated in “Application to the Navier–Stokes equations” section with an application to the Navier–Stokes system in critical \(L_q\)-spaces.

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Prüss, J., Wilke, M. Addendum to the paper “On quasilinear parabolic evolution equations in weighted \(L_p\)-spaces II”. J. Evol. Equ. 17, 1381–1388 (2017). https://doi.org/10.1007/s00028-017-0382-6

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  • DOI: https://doi.org/10.1007/s00028-017-0382-6

Keywords

  • Quasilinear parabolic evolution equations
  • Critical spaces
  • Navier–Stokes

Mathematics Subject Classification

  • Primary 35K90
  • 35B30
  • Secondary 35B40