Vol. 314, No. 1, 2021

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Correction to the article Local estimates on two linear parabolic equations with singular coefficients

Qi S. Zhang

Vol. 314 (2021), No. 1, 253–258

Correction to Pacific Journal of Mathematics 223:2 (2006) 367–396

Abstract

The purpose of the corrigendum is to fill in a missing term in Theorem 1.7 and Lemma 3.3 in the paper Pacific J. Math. 223:2 (2006), 367–396. This is due to the use of a formula in a cited reference, which omitted a term. The main conclusion that local solutions of a certain linearized Navier–Stokes equation have bounded spatial gradient is intact. This includes bounded local Leray–Hopf solutions to the Navier–Stokes equation without condition on the pressure.

Keywords
Navier–Stokes, local representation formula, Kato class
Mathematical Subject Classification
Primary: 35Q30
Milestones
Received: 21 October 2020
Revised: 9 July 2021
Accepted: 9 July 2021
Published: 15 October 2021
Authors
Qi S. Zhang
Department of Mathematics
University of California, Riverside
United States