Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2020; 57(6): 1393-1408

Online first article September 9, 2020      Printed November 30, 2020

https://doi.org/10.4134/BKMS.b191054

Copyright © The Korean Mathematical Society.

Gevrey regularity and time decay of the fractional Debye-H\"uckel system in Fourier-Besov spaces

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.

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