In this paper, we study the Cauchy problem of the generalized Poisson–Nernst–Planck equations modeling the anomalous (normal) diffusion and transport of charged particles. Making full use of the algebraical structure of the equations and the Fourier localization technique, we obtain a new global well-posedness result without requiring the summation of initial densities of a negatively and positively charged species are small enough.

中文翻译：

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广义Poisson-Nernst-Planck方程的大解的整体存在

在本文中，我们研究了广义Poisson-Nernst-Planck方程的Cauchy问题，该方程对带电粒子的异常（正态）扩散和传输进行了建模。充分利用方程的代数结构和傅立叶定位技术，我们获得了新的全局适定性结果，而无需将带负电和带正电物质的初始密度求和足够小。