Long time solutions for a Burgers-Hilbert equation via a modified energy method
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- by John K. Hunter, Mihaela Ifrim, Daniel Tataru and Tak Kwong Wong PDF
- Proc. Amer. Math. Soc. 143 (2015), 3407-3412 Request permission
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.References
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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
- MR Author ID: 267163
- 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
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 3407-3412
- MSC (2010): Primary 35L60
- DOI: https://doi.org/10.1090/proc/12215
- MathSciNet review: 3348783