具有大初值和真空的Navier-Stokes-Maxwell方程组强解的全局存在性和唯一性

Existence and uniqueness of global strong solutions to the Navier-Stokes-Maxwell system with large initial data and vacuum

本文研究了一维空间中可压缩Navier-Stokes方程组,通过Lorentz力耦合Maxwell方程组的初边值问题,得到了在大初始值且带真空的情形下强解的全局存在性和唯一性.本文结果可视为带真空和大初值的强解全局存在性的第一个结果.

In this paper, we investigate the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in one space dimension.The global existence and uniqueness of strong solutions with large initial data are established when there is initial vacuum. Our result may be the first result about the global strong solution with large initial data and vacuum.