SUPPRESSION OF BLOW-UP IN PATLAK-KELLER-SEGEL VIA SHEAR FLOWS (vol 49, pg 4722, 2017)

There is unfortunately a small gap in the original proof of one of the theorems in "Suppression of Blow-Up in Patlak-Keller-Segel Via Shear Flows" [Bedrossian and He, SIAM J. Math. Anal., 49 (2017), pp. 4722-4766]. Specifically, the proof of Theorem 2(b), the case T x R-2, has an error in Lemma 4.1, the control on the free energy. The application of Sard's theorem incorrectly ignores boundary contributions at infinity and we do not see a way to justify the stated inequality rigorously. The correction is not difficult but does require a slightly different approach to the problem of controlling the two-dimensional free energy. Below we outline the corrected proof.