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

Sarria, Alejandro; Saxton, Ralph

doi:10.1090/S0033-569X-2015-01378-3

Authors: Alejandro Sarria and Ralph Saxton
Journal: Quart. Appl. Math. 73 (2015), 55-91
MSC (2010): Primary 35B44, 35B10, 35B65, 35Q35
DOI: https://doi.org/10.1090/S0033-569X-2015-01378-3
Published electronically: January 21, 2015
MathSciNet review: 3322726
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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.

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