报告题目：Stability of the planar rarefaction wave to three-dimensional compressible model of viscous ions motion

报告时间：2023年10月17日 上午10：00

报告地点：南湖校区教学科研楼516

主办单位：数学与统计学院

报告人： 黎野平

报告人简介：南通大学理学院教授、博士研究生导师、湖北“楚天学者”特聘教授。先后在武汉大学和香港中文大学获理学硕士学位和博士学位。主要致力于非线性偏微分方程的研究，尤其是来自物理、材料、生物和医学等自然科学中的各类非线性偏微分方程和非线性耦合方程组。在《Mathematical Models and Methods in Applied Sciences》，《SIAM Journal of Mathematical Analysis》，《Journal of Differential Equations》和《Calculus of Variations and Partial Differential Equations》等国际、国内的重要学术期刊杂志上发表论文90余篇，其中SCI80余篇。同时，主持完成国家自然科学基金3项和教育部博士点博导专项、上海市教委创新项目以及江苏省自然科学基金等各类科研项目多项；现在正主持国家自然科学基金面上项目1项和参加国家自然科学基金重点项目1项和面上项目2项。

摘要：In this talk, I am going to present the time-asymptotic behavior of strong solutions to the compressible Navier-Stokes-Poisson equations in three dimension. The equation models the motion of viscous ions and plays important roles in the study of self-gravitational viscous gaseous stars and in the simulations of charged particles in semiconductor devices and plasmas physics. This talk mainly establishes the stability and precise large-time behavior of perturbations near the planar rarefaction wave to three-dimensional isentropic compressible Navier-Stokes-Poisson equations. The results presented in this paper are new. Previous studies focused on the one-dimensional compressible Navier-Stokes-Poisson equations and little has been done for the multi-dimensional case. In order to prove the desired asymptotic stability, we takes into account both the effect of the self-consistent electrostatic potential and the decay rate of the planar rarefaction wave. Due to the complexity of the nonlinearity and the effect of the self-consistent electric field, the proof involves highly non-trivial a priori bounds. This is a joint work with Prof. Zhen Luo and Prof. Jiahong Wu.