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

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