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International Mathematics Research Notices Advance Access originally published online on February 23, 2009
International Mathematics Research Notices (2009) 2009:2508-2518, doi:10.1093/imrn/rnp023 published on June 28, 2009
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© The Author 2009. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Regularity Criteria for the Viscous Camassa–Holm Equations

Yong Zhou1 and Jishan Fan2

1 Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China
2 Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, Jiangsu, China

Correspondence: Correspondence to be sent to: yzhoumath{at}zjnu.edu.cn

In this paper, we consider the viscous n-dimensional Camassa–Holm equations in the whole space. Various regularity criteria for the strong solution are established. As a corollary, we show the existence of a global smooth solution when Formula .

Communicated by Prof. Michael Struwe


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