The role of initial curvature in solutions to the generalized inviscid Proudman-Johnson equation

Abstract

In Sarria and Saxton (2013), we derived representation formulae for spatially periodic solutions to the generalized, inviscid Proudman-Johnson equation and studied their regularity for several classes of initial data. The purpose of this paper is to extend these results to larger classes of functions including those having arbitrary local curvature near particular points in the domain.