Commutator estimates in Besov-Morrey spaces with applications to the well-posedness of the Euler equations and ideal MHD system

Jiang Xu; Yong Zhou

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arXiv · 1303.6005

Commutator estimates in Besov-Morrey spaces with applications to the well-posedness of the Euler equations and ideal MHD system

Jiang Xu·Yong Zhou

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Abstract

We develop commutator estimates in the framework of Besov-Morrey spaces, which are modeled on Besov spaces and the underlying norm is of Morrey space rather than the usual $L^{p}$ space. As direct applications of commutator estimates, we establish the local well-posedness and blow-up criterion of solutions in Besov-Morrey spaces for the incompressible Euler equations and ideal MHD system. Main analysis tools are the Littlewood-Paley decomposition and Bony's para-product formula.

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Jiang Xu, Yong Zhou. 2013-03-25. Commutator estimates in Besov-Morrey spaces with applications to the well-posedness of the Euler equations and ideal MHD system. https://arxiv.org/abs/1303.6005

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