Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type |
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Authors: | Ryo Takada |
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Institution: | (1) Mathematical Institute, Tohoku University, 6-3 Aoba-ku, Sendai 980-8578, Japan |
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Abstract: | 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 . For the proof, we establish the Beale-Kato-Majda type logarithmic inequality and commutator type estimates in our weak spaces.
Abbreviate title: Euler equations in Besov spaces of weak type |
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Keywords: | :" target="_blank">: Euler equations Local existence blow-up criterion Besov spaces of weak type Littlewood-Paley decomposition commutator estimates |
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