Large Solutions to the Generalized Debye-Hückel System in Fourier-Besov Spaces  

Debye-Huckel系统的部分大初值整体解

作　　者：XIAO Weiliang ZHOU Xuhuan 肖伟梁;周需焕(南京财经大学应用数学学院,江苏南京210023;南京警察学院基础部,江苏南京210023)

机构地区：[1]School of Applied Mathematics,Nanjing University of Finance and Economics,Nanjing,210023,P.R.China [2]Department of Basic,Nanjing Police University,Nanjing,Jiangsu,210023,P.R.China

出　　处：《数学进展》2024年第5期1059-1070,共12页Advances in Mathematics（China）

基　　金：Supported by Natural Science Foundation of Jiangsu Province(No.BK20200587)。

摘　　要：The special structure in some coupled equations makes it possible to drop partial smallness assumption of the initial data to gain the global well-posedness.In this paper,we study the Cauchy problem for generalized Debye-Hückel system in Fourier-Besov spaces.Under more generalized index range,we obtain the global solution with small initial data and local solution with arbitrary initial.Besides,by constructing some weighted function,we prove that the global well-posedness still holds under the small assumption of the charge of initial data.Thus we show that although the initial densities and the hole in electrolytes are large,the equation is still global well-posedness.一些耦合方程的特殊结构可通过去掉初值的部分小假设获得整体适定性.本文研究Fourier-Besov空间中广义Debye-Huckel系统的初值问题,在更一般的指标范围内得到方程的小初值整体解和大初值局部解.并且通过构造加权函数,进一步得到初值的差很小时整体解依然存在.这表明,尽管初始密度和电解质中的空洞很大,方程仍然是整体适定的.

关 键 词：Debye-Huckel system solution with large initial data Fourier-Besov space 

分 类 号：O175.4[理学—数学]