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

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


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