发表机构
School of Mathematics and Information Science, Baoji University of Arts and Sciences; School of Mathematics and Statistics, Jiangsu Normal University（宝鸡文理学院数学与信息科学学院; 江苏师范大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明NS-NPP方程在Fujita-Kato型大初始数据下存在唯一全局解，放宽了正负电荷密度之和的小性条件。
AI 中文摘要
本文证明了具有某些大的Fujita-Kato型初始数据的NS-NPP方程Cauchy问题的全局适定性。具体地，我们证明了存在两个正常数$c_{0}$和$C_{0}$，使得若初始数据$(u_{0}, N_{0}, P_{0})$满足以下条件：\begin{equation*} \left(\\|u_0\\|_{\dot{H}^{-1+\frac{d}{2}}}+\\|N_{0}-P_{0}\\|_{\dot{H}^{-2+\frac{d}{2}}}\right)\exp\left\{C_{0}\big(\\|N_{0}+P_{0}\\|_{\dot{H}^{-2+\frac{d}{2}}}^2+1\big)\right\} \leq c_{0}, \end{equation*} 则NS-NPP方程存在唯一的全局解。该结果表明，在Sobolev空间的框架下，无需对正负电荷初始粒子密度之和施加任何小性条件，即可获得解的全局存在性。
英文摘要
In this paper, we prove the global well-posedness of the Cauchy problem for the NS-NPP equations with some large Fujita-Kato type initial data. Specifically, we show that there exist two positive constants $c_{0}$ and $C_{0}$ such that if the initial data $(u_{0}, N_{0}, P_{0})$ satisfies the following condition: \begin{equation*} \left(\|u_0\|_{\dot{H}^{-1+\frac{d}{2}}}+\|N_{0}-P_{0}\|_{\dot{H}^{-2+\frac{d}{2}}}\right)\exp\left\{C_{0}\big(\|N_{0}+P_{0}\|_{\dot{H}^{-2+\frac{d}{2}}}^2+1\big)\right\} \leq c_{0}, \end{equation*} then the NS-NPP equations admits a unique global solution. This result implies global existence of solutions without any smallness conditions imposed on the sum of initial particle densities of negative and positive electric charge in the framework of Sobolev spaces.
Comments18 pages
