应兰州大学数学与统计学院邀请，华侨大学于海波副教授将于2025年9月9日-9月12日访问我校，并于2025年9月10日上午10:00-11:00，9月11日上午10:00-11:00分别作线下学术报告。欢迎广大师生参加！

Title: Global well-posedness and decay of compressible gas with zero heat conductivity at high pressures

时间：2025年9月10日(星期三)上午10:00-11:00

地点：城关校区凌云楼631

Abstract: At high pressures the viscosities of gases increase with increasing pressure.Based on the fact, we consider the Cauchy problem to the three-dimensional full compressible Navier-Stokes system with zero heat conductivity when the viscosity coefficients are proportional to the pressure. Through some delicate \emph{a priori} assumptions, we prove that strong solution exists globally in time at high pressures. In order to derive energy-dissipationinequality of solution, we construct a new equation for the gradient of pressure by combining the gradient of energy equation and the momentum equations. This kind of inequality leads us to the optimal time-decay rate of the solution in $L^2$. Especially, the initial data can be arbitrarily large, and the initial density and initial pressure are allowed to have large oscillations.

Title:Optimal decay rates of low-energy strong solution to the 3D isentropic compressible Navier-Stokes equations

时间：2025年9月11日(星期四)上午10:00-11:00

地点：城关校区凌云楼631

Abstract:This paper concerns the optimal time-decay rates of the 3D isentropic compressible Navier-Stokes equations. For the case when the initial energy is small, global existence and optimal decay rates of strong solution are obtained under the condition that $L^p$-norm of the initial perturbation is bounded for $1\leq p<2$. In order to derive energy-dissipation inequality of solution, we construct a new equation for the gradient of density by combining the gradient of mass equation and the momentum equations. This kind of inequality leads us to some preliminary time-decay rates (not necessarily optimal), which together with Duhamel's principle implies the optimal time-decay rates. Compared with previous results, the Sobolev norms of spatial derivatives of initial data can be arbitrarily large.

报告人简介

于海波，男，华侨大学副教授。2014年于厦门大学获理学博士学位。主要研究内容为可压缩NS、MHD、NSP等流体动力学方程的整体适定性理论及最优衰减估计。近年来在Nonlinearity，JDE等期刊上发表SCI论文20余篇。

数学与统计学院

萃英学院

2025年9月8日