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We introduce Besov type function spaces, based on the weak L p -spaces instead of the standard L p -spaces, and prove a local-in-time unique existence and a blow-up criterion of solutions in those spaces for the Euler equations of perfect incompressible fluid in $${\mathbb{R}}^n , n \geq 3$$ . For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator type estimates in our weak spaces.
Journal of Evolution Equations – Springer Journals
Published: Nov 1, 2008
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