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Long time solutions for a Burgers-Hilbert equation via a modified energy method


Authors: John K. Hunter, Mihaela Ifrim, Daniel Tataru and Tak Kwong Wong
Journal: Proc. Amer. Math. Soc. 143 (2015), 3407-3412
MSC (2010): Primary 35L60
DOI: https://doi.org/10.1090/proc/12215
Published electronically: April 16, 2015
MathSciNet review: 3348783
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Abstract: We consider an initial value problem for a quadratically nonlinear inviscid Burgers-Hilbert equation that models the motion of vorticity discontinuities. We use a modified energy method to prove the existence of small, smooth solutions over cubically nonlinear time-scales.


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Additional Information

John K. Hunter
Affiliation: Department of Mathematics, University of California at Davis, Davis, California 95616
Email: hunter@math.davis.edu

Mihaela Ifrim
Affiliation: Department of Mathematics, McMaster University, West Hamilton, Ontario L8S 4L8, Canada
Email: ifrim@math.berkeley.edu

Daniel Tataru
Affiliation: Department of Mathematics, University of California at Berkeley, Berkeley, California 94704
Email: tataru@math.berkeley.edu

Tak Kwong Wong
Affiliation: Department of Mathematics, University of Pennsylvania, 3451 Walnut St., Philadelphia, Pennsylvania 19104
Email: takwong@math.upenn.edu

DOI: https://doi.org/10.1090/proc/12215
Received by editor(s): February 15, 2013
Received by editor(s) in revised form: March 30, 2013
Published electronically: April 16, 2015
Additional Notes: The first author was partially supported by the NSF under grant number DMS-0072343.
The third author was partially supported by NSF grant DMS-0801261 as well as by the Simons Foundation
Communicated by: Joachim Krieger
Article copyright: © Copyright 2015 American Mathematical Society

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