Erratum to “Navier–Stokes equations in a curved thin domain, Part III: thin-film limit”

Abstract

There are two flaws in the third part [3] of our study on the Navier--Stokes equations in a curved thin domain. The first one is that the form of Ladyzhenskaya's inequality on a closed surface taken from the arXiv version [2] of the second part of our study is incorrect. The second one is that a wrong claim is used in the proofs of lemmas in [3, Section 6.3] which give estimates for the weighed potential part of a tangential surface vector field. This erratum corrects these flaws.