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

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• 作者：Jihong Zhao ^{jihzhao@163.com zhaojih@nwsuaf.edu.cn}
• 关键词：Drift-diffusion system ; Mild solutions ; Gevrey regularity ; Decay
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 April 2017
• 年：2017
• 卷：448
• 期：2
• 页码：1265-1280
• 全文大小：434 K
• 卷排序：448

文摘

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<2n1<p<2n and 1≤r≤∞1≤r≤∞, where Λ1Λ1 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.