On the Cauchy problem for the Degasperis-Procesi equation
Authors:
Guilong Gui and Yue Liu
Journal:
Quart. Appl. Math. 69 (2011), 445-464
MSC (2000):
Primary 35L15, 35G25, 35Q58
DOI:
https://doi.org/10.1090/S0033-569X-2011-01216-5
Published electronically:
April 5, 2011
MathSciNet review:
2850740
Full-text PDF Free Access
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Abstract: We establish here the local well-posedness for the Degasperis-Procesi equation in the Besov spaces. We also determine some blow-up criteria of the strong solutions and investigate the nonexistence of smooth solitary-wave solutions.
References
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- G. Rodriguez-Blanco, On the Cauchy problem for the Camassa-Holm equation. Nonlinear Anal. 46 (2001), 309–327. MR 1851854 (2002i:35172)
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- Z. Yin, On the Cauchy problem for an integrable equation with peakon solutions. Illinois J. Math. 47 (2003), 649–666. MR 2007229 (2004g:35217)
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Additional Information
Guilong Gui
Affiliation:
Department of Mathematics, Jiangsu University, Zhenjiang 212013, Jiangsu, People’s Republic of China
Address at time of publication:
Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email:
glgui@amss.ac.cn
Yue Liu
Affiliation:
Department of Mathematics, University of Texas, Arlington, Texas 76019
Email:
yliu@uta.edu
Keywords:
Local well-posedness,
blow-up,
Degasperis-Procesi equation,
peakons,
Besov spaces.
Received by editor(s):
November 15, 2009
Published electronically:
April 5, 2011
Additional Notes:
The work of the first author was supported in part by the NSF of China under Grant 11001111, and Grants 10JDG141 and 10JDG157.
The work of the second author was partially supported by the NSF grant DMS-0906099 and the NHARP grant-003599-0001-2009. Both authors would like to thank the referee for constructive suggestions and comments.
Article copyright:
© Copyright 2011
Brown University
The copyright for this article reverts to public domain 28 years after publication.
