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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Local regularity and decay estimates of solitary waves for the rotation-modified Kadomtsev-Petviashvili equation


Authors: Robin Ming Chen, Yue Liu and Pingzheng Zhang
Journal: Trans. Amer. Math. Soc. 364 (2012), 3395-3425
MSC (2010): Primary 35Q53, 76B03, 75B15, 76B25
Published electronically: February 20, 2012
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Abstract: This paper is mainly concerned with the local low regularity of
solutions and decay estimates of solitary waves to the rotation-modified
Kadomtsev-Petviashvili (rmKP) equation. It is shown that with negative dispersion, the rmKP equation is locally well-posed for data in $ H^{s_1,s_2}(\mathbb{R}^2)$ for $ s_1>-\frac {3}{10}$ and $ s_2\geq 0$, and hence globally well-posed in the space $ L^2$. Moreover, an improved result on the decay property of the solitary waves is established, which shows that all solitary waves of the rmKP equation decay exponentially at infinity.


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Additional Information

Robin Ming Chen
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: chenm@math.umn.edu, mingchen@pitt.edu

Yue Liu
Affiliation: Department of Mathematics, University of Texas at Arlington, Arlington, Texas 76019-0408
Email: yliu@uta.edu

Pingzheng Zhang
Affiliation: Department of Mathematics, Jiangsu University, Jiangsu 212013, People’s Republc of China
Email: pzzhang@ujs.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05383-9
PII: S 0002-9947(2012)05383-9
Keywords: Kadomtsev-Petviashvili, rotation, Cauchy problem, well-posedness, solitary wave
Received by editor(s): December 21, 2009
Received by editor(s) in revised form: April 19, 2010
Published electronically: February 20, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.