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Low regularity solutions, blowup, and global existence for a generalization of Camassa–Holm‐type equation
Author(s) -
Liu Xingxing,
Yin Zhaoyang
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2945
Subject(s) - mathematics , camassa–holm equation , generalization , sobolev space , novikov self consistency principle , type (biology) , space (punctuation) , order (exchange) , mathematical analysis , pure mathematics , integrable system , computer science , ecology , finance , economics , biology , operating system
We consider a generalization of Camassa–Holm‐type equation including the Camassa–Holm equation and the Novikov equation. We mainly establish the existence of solutions in lower order Sobolev spaceH s( R ) with 1 < s ≤ 3 2 . Then, we present a precise blowup scenario and give a global existence result of strong solutions. Copyright © 2013 John Wiley & Sons, Ltd.