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Communications on Pure and Applied Analysis (CPAA)
 

On the Lagrangian averaged Euler equations: local well-posedness and blow-up criterion

Pages: 1809 - 1823, Volume 11, Issue 5, September 2012      doi:10.3934/cpaa.2012.11.1809

 
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Xinwei Yu - Department of Mathematical and Statistical Sciences, University of Alberta, 632 CAB, Edmonton, AB T6G 2G1, Canada (email)
Zhichun Zhai - Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada (email)

Abstract: In this article we study local and global well-posedness of the Lagrangian Averaged Euler equations. We show local well-posedness in Triebel-Lizorkin spaces and further prove a Beale-Kato-Majda type necessary and sufficient condition for global existence involving the stream function. We also establish new sufficient conditions for global existence in terms of mixed Lebesgue norms of the generalized Clebsch variables.

Keywords:  Global existence, level sets, vortex patch, Euler equations, Triebel-Lizorkin spaces.
Mathematics Subject Classification:  Primary: 76B03; Secondary: 35Q35, 35B40.

Received: March 2011;      Revised: August 2011;      Available Online: March 2012.

 References