Gevrey regularity of mild solutions to the parabolic–elliptic system of drift-diffusion type in critical Besov spaces

Abstract

This paper is devoted to studying analyticity of mild solutions to the parabolic–elliptic system of drift-diffusion type with small initial data in critical Besov spaces. More precisely, by using multilinear singular integrals and Fourier localization argument, we show that global-in-time mild solutions are Gevrey regular, i.e., (etΛ1v,etΛ1w)∈L˜t∞B˙p,r−2+np(Rn)∩L˜t1B˙p,rnp(Rn) for all 1<p<2n and 1≤r≤∞, where Λ1 is the Fourier multiplier whose symbol is given by |ξ|1=∑i=1n|ξi|. As a corollary, we obtain decay estimates of mild solutions in critical Besov spaces without using cumbersome recursive estimation of higher-order derivatives.