Local regularity and decay estimates of solitary waves for the rotation-modified Kadomtsev-Petviashvili equation
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- by Robin Ming Chen, Yue Liu and Pingzheng Zhang PDF
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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 $s_2\geqslant 0$, 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.References
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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
- Received by editor(s): December 21, 2009
- Received by editor(s) in revised form: April 19, 2010
- Published electronically: February 20, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 3395-3425
- MSC (2010): Primary 35Q53, 76B03, 75B15, 76B25
- DOI: https://doi.org/10.1090/S0002-9947-2012-05383-9
- MathSciNet review: 2901218