郝成春的个人主页 | Chengchun HAO's Homepage
研究员、博士生导师,中国科学院数学与系统科学研究院 数学研究所 | Professor, Institute of Mathematics, AMSS, CAS
中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
题目/Title: Optimal time-decay estimates for the compressible Navier-Stokes-Poisson system in the critical $L^{p}$ framework
报告人:史维选(南京航空航天大学)时间:2019年12月19日 星期四 14:00-15:00
地点:南楼N602
摘要:The compressible Navier-Stokes-Poisson system takes the form of usual Navier -Stokes equations coupled with the self-consistent Poisson equation, which is used to simulate the transport of charged particles under the electric field of electrostatic potential force. In this paper, we focus on the large time behavior of global strong solutions in the $L^{p}$ Besov spaces of critical regularity. By exploring the dissipative effect arising from Poisson potential, we posed the new regularity assumption of low frequencies and then establish a sharp time-weighted inequality, which leads to the optimal time-decay estimates of the solution. Indeed, we see that the decay of density is faster at the half rate than that of velocity, which is a different ingredient in comparison with the situation of usual Navier-Stokes equations. Our proof mainly depends on tricky and non classical Besov product estimates with respect to various Sobolev embeddings.
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