Addendum to the Paper "On Quasilinear Parabolic Evolution Equations in Weighted $L_p$-Spaces II"

TL;DR

This paper extends a key theorem on quasilinear parabolic evolution equations in weighted Lp-spaces, providing an improved result that enhances the analysis of the Navier-Stokes system in critical Lq-spaces.

Contribution

It offers a significant extension of Theorem 2.1 from a previous work, broadening the applicability to critical Lq-spaces for Navier-Stokes equations.

Findings

Extended Theorem 2.1 with broader applicability

Demonstrated importance through Navier-Stokes application

Enhanced understanding of quasilinear parabolic equations in weighted spaces

Abstract

This note is devoted to a small, but essential, extension of Theorem 2.1 of our recent paper [6]. The improvement is explained in Section 1 and proved in Section 2. The importance of the extension is demonstrated in Section 3 with an application to the Navier-Stokes system in critical $L_q$-spaces.