Journal
IMA JOURNAL OF APPLIED MATHEMATICS
Volume 80, Issue 3, Pages 906-930Publisher
OXFORD UNIV PRESS
DOI: 10.1093/imamat/hxu032
Keywords
the modified CH and DP equations; local well-posedness; Besov space; conservation laws; blow-up scenario; blow-up phenomena; blow-up rate; persistence properties
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Funding
- CPSF [2012M520007, 2013T60086]
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We mainly study the Cauchy problem of modified Camassa-Holm and Degasperis-Procesi equations. First, we establish the local well-posedness for the equation in Besov space. Secondly, we derive the conservation laws and a precise blow-up scenario. Moreover, we prove the existence of blow-up solutions and obtain its blow-up rate, provided the initial data satisfy certain conditions. Finally, we present the persistence properties of the equation.
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