讲座题目: Stability and instability for a generic non-conservative compressible two-fluid model

讲座摘要: We are concerned with stability and instability of the steady state (1,0, 1, 0) for a generic non–conservative compressible two–fluid model in R^3. Under the assumption that the initial fraction densities are close to the constant state (1,1) in H^3\cap\dot B^{s}_{1,\infty} and the initial velocities are small in H^2\cap\dot B^{s}_{1,\infty} with s\in [0,1], it is shown that \frac{1}{2} is the critical value of s on the stability of the model in question. More precisely, when 0\leq s<\frac{1}{2}, the steady state (1,0, 1, 0) is nonlinearly globally stable; and conversely, the steady state (1,0, 1, 0) is nonlinearly unstable in the sense of Hadamard when \frac{1}{2}<s\le 1. Furthermore, for the critical case s=\frac{1}{2}, if the initial data satisfy additional regularity assumption, then the steady state (1,0, 1, 0) is nonlinearly globally stable.

讲座时间：2023年4月20日（周四）下午16:00

讲座方式：线上开展（腾讯会议，会议号：769 437 019）

嘉宾简介：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，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.、Nonlineaity、 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）。