On analyticity rate estimates to the magneto-hydrodynamic equations in Besov-Morrey spaces.

In this article, we establish higher-order regularizing rate estimates of solutions to generalized magneto-hydrodynamic equations in Morrey spaces with initial data $(u_{0}, d_{0})$ in Besov-Morrey spaces $\dot {\mathbf{N}}_{r, \lambda,\infty}^{-s}\times\dot{\mathbf{N}}_{r, \lambda , \infty}^{-s}$, where $n\geq2$, $1\leq r<\infty$, $0\leq\lambda< n$, $r>n-\lambda$, $\frac {1}{2}+\frac{n-\lambda}{4r}<\sigma< 1+\frac{n-\lambda}{4r}$, and $s=2\sigma-1-\frac{n-\lambda}{r}$, for which under some smallness condition, the solution of the Cauchy problem is analytic in the spatial variable. Our class of initial data contains strongly singular functions and measures and extends the ones in early work. [ABSTRACT FROM AUTHOR]