报告人：张映辉 (广西师范大学)

时间：2021年6月12日8:30开始

地点：理科楼LA106

摘要:This paper is concerned with the Cauchy problem of the 3D compressible bipolar Navier-Stokes-Poisson (BNSP) system, and our main purpose is three-fold: First, under the assumption that $H^l\cap L^1$($l\geq 3$)-norm of the initial data is small, we prove the optimal time decay rates of the solution as well as its all-order spatial derivatives from one-order to the highest-order, which are the same as those of the compressible Navier-Stokes equations and the heat equation. Second, for well-chosen initial data, we also show the lower bounds on the decay rates. Therefore, our time decay rates are optimal. Third, we give the explicit influences of the electric field on the qualitative behaviors of solutions, which are totally new as compared to the results for the compressible Navier-Stokes (NS) system. This phenomenon is the most important difference from the compressible Navier-Stokes equations. More precisely, we show that the densities of the BNSP system converge to their corresponding equilibriums at the same $L^2$-rate $(1+t)^{-\frac{3}{4}}$ as the compressible Navier-Stokes equations, but the momentums of the BNSP system and the difference between two densities decay at the $L^2$-rate $(1+t)^{-\frac{3}{2}(\frac{1}{p}-\frac{1}{2})}$ and $(1+t)^{-\frac{3}{2}(\frac{1}{p}-\frac{1}{2})-\frac{1}{2}$ with $1\leq p\leq \frac{3}{2}$, respectively, which depend directly on the initial low frequency assumption of electric field, namely, the smallness of $\|\nabla\phi_0\|_{L^p}$.

简介:张映辉，教授、博士生导师，广西省杰出青年基金获得者，广西高等学校中青年骨干教师，广西师范大学A类漓江学者，美国佐治亚理工学院和加拿大不列颠哥伦比亚大学访问学者，现任广西师范大学太阳成集团tyc539副经理。主要研究方向为偏微分方程理论及其应用。

邀请人：穆春来   王华桥

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