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On the well-posedness of the Euler equations in the Triebel-Lizorkin spaces

✍ Scribed by Dongho Chae

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
212 KB
Volume
55
Category
Article
ISSN
0010-3640

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✦ Synopsis

Abstract

We prove local‐in‐time unique existence and a blowup criterion for solutions in the Triebel‐Lizorkin space for the Euler equations of inviscid incompressible fluid flows in ℝ^n^, n ≥ 2. As a corollary we obtain global persistence of the initial regularity characterized by the Triebel‐Lizorkin spaces for the solutions of two‐dimensional Euler equations. To prove the results, we establish the logarithmic inequality of the Beale‐Kato‐Majda type, the Moser type of inequality, as well as the commutator estimate in the Triebel‐Lizorkin spaces. The key methods of proof used are the Littlewood‐Paley decomposition and the paradifferential calculus by J. M. Bony. © 2002 John Wiley & Sons, Inc.

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