Yiwen Cui, Weiliang Xiao Nanjing University of Finance and Economics; Nanjing University of Finance and Economics
Abstract : In this paper we mainly study existence and regularity of mild solutions to the parabolic-elliptic system of drift-diffusion type with small initial data in Fourier-Besov spaces. To be more detailed, we will explain that global-in-time mild solutions are well-posed and Gevrey regular by means of multilinear singular integrals and Fourier localization argument. Furthermore, we can get time decay rate estimate of mild solutions in Fourier-Besov spaces.
Keywords : Debye-H\"uckel system, Gevrey regularity, time decay, Fourier-Besov spaces
MSC numbers : Primary 42B37, 35Q35, 35K55, 76B03
Supported by : The research was supported by the NNSF of China under grant No. 11601223.