Article Contents

2012, Volume 11, Issue 5: 1809-1823. Doi: 10.3934/cpaa.2012.11.1809

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

Xinwei Yu^1, and
Zhichun Zhai^2,

1.
Department of Mathematical and Statistical Sciences, University of Alberta, 632 CAB, Edmonton, AB T6G 2G1
2.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1

Received: March 2011

Revised: August 2011

Published: September 2012

Abstract / Introduction Related Papers Cited by

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:

Mathematics Subject Classification: Primary: 76B03; Secondary: 35Q35, 35B40.

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