Global existence and Gevrey analyticity of the Debye-Huckel system in critical Besov-Morrey spaces

The paper deals with the Cauchy problem of the Debye-Huckel system in homogeneous Besov-Morrey spaces. By using the smoothing effect of the heat semigroup and the Littlewood-Paley theory, we obtain the global existence of solutions for small initial data in the critical Besov-Morrey spaces N-p,h,infinity(center dot)-2+d/p(R-d)xN(p,h,infinity)(center dot)(-2+d/p)(R-d) with d/2<p<infinity and 1 <= h <= p. . Moreover, we demonstrate that the solutions obtained are analytic in a Gevrey class. Finally, as a consequence of Gevrey analyticity result, we get time decay estimates of solutions in critical Besov-Morrey spaces.