报告人：张映辉（广西师范大学）

时 间：2023年6月15日上午9:30

地 点：海韵园实验楼106报告厅

内容摘要:

We investigate vanishing capillarity limit problem of a generic compressible two--fluid model with common pressure ($P^+=P^-$) in $\mathbb{R}^3$. Under some smallness assumptions, Evje--Wang--Wen [Arch Rational Mech Anal 221:1285--1316, 2016] obtained the global solution and its optimal decay rate for the 3D compressible two--fluid model with unequal pressures $P^+\neq P^-$. More precisely, the capillary pressure $f(\alpha^-\rho^-)=P^+-P^-\neq 0$ is taken into account, and is assumed to be a strictly decreasing function near the equilibrium. As pointed out by Evje--Wang--Wen, this assumption played a key role in their analysis and appeared to have an essential stabilization effect on the model. Recently, based on the result of Evje--Wang--Wen, Lai--Wen--Yao [Discrete Cont. Dyn--B, 22(4):1361--1392,2017] studied the corresponding vanishing capillarity limit problem. However, up to now, the vanishing capillarity limit of the 3D compressible two--fluid model with common pressure has remained a challenging open problem since the system is partially dissipative and the coupling effects between two fluids are very strong. In the present work, by exploiting the dissipation structure of the model and employing several key observations, it is shown that the unique smooth solution of the generic compressible two--fluid model exists for all time, and converges globally in time to the unique smooth solution of the compressible two--fluid Navier--Stokes equations, as the capillary coefficient $\sigma$ tends to zero. Moreover, as a by--product, the convergence rate estimates with respect to the capillary coefficient $\sigma$ for any given positive time are also obtained. To the best of our knowledge, we establish the first result on the vanishing capillarity limit of the 3D compressible two--fluid model with common pressure.

个人简介：

张映辉，教授，博士生导师，广西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，广西高校数学模型及其应用重点实验室主任，广西师范大学应用数学研究所所长，现任广西师范大学数学与统计学院副院长。主要研究方向为偏微分方程理论及其应用。主持国家自然科学基金面上项目、青年项目和天元项目各1项，广西杰出青年科学基金、博士后基金等多项省部级课题；在SIAM J. Math. Anal., J. London Math. Soc., Indiana U. Math. J., Nonlinearity, J. Differ. Equations, 中国科学(英文版)等期刊上发表学术论文30余篇；出版英文学术专著2部；获省自然科学奖和市科技进步奖各1项。获威立（Wiley）出版社2021-2022年度论文最高引用（率）奖（Top Cited Article 2021-2022）。

联系人：王焰金