Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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


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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Additional Information

Alejandro Sarria
Affiliation: Department of Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309
Email: alejandro.sarria@colorado.edu

Ralph Saxton
Affiliation: Department of Mathematics, University of New Orleans, New Orleans, Louisiana 70148
Email: rsaxton@uno.edu

DOI: https://doi.org/10.1090/S0033-569X-2015-01378-3
Received by editor(s): December 21, 2012
Received by editor(s) in revised form: August 9, 2013
Published electronically: January 21, 2015
Article copyright: © Copyright 2015 Brown University


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