题    目：Asymptotic stability of the stationary solution to an out-flow problem for the Navier-Stokes-Korteweg equations of compressible fluids

报告人：黎野平 教授

主持人：高利新 教授

时    间： 2020年10月15日下午15：30——16：30

地    点：数理学院三号楼3B201

【摘要】 In this talk, We mainly present the large-time behavior of solutions to an out-flow problem in one-dimensional half space for the Navier-Stokes-Korteweg equations which models compressible fluids with internal capillarity. Applying the center manifold theory, we prove the existence of the stationary solution under a smallness condition on the boundary data and a proper relation between the capillary coefficient κ and Mach number M+ at far field. Then making use of the energy method and the inequality of Poincar´e type, we show that the stationary solution is asymptotically stable under smallness assumptions on the boundary data and the initial perturbation in Sobolev space. This is a joint work with Peicheng Zhu.

黎野平教授简介

黎野平，华东理工大学理学院教授、博士研究生导师、湖北“楚天学者”特聘教授。先后在武汉大学和香港中文大学获理学硕士学位和博士学位。主要致力于非线性偏微分方程的研究，尤其是来自物理、材料、生物和医学等自然科学中的各类非线性偏微分方程和非线性耦合方程组。在《Mathematical Models and Methods in Applied Sciences》，《SIAM J. Math.Anal.》，《Journal of Differential Equations》和《Communications in Mathematical Sciences》等国际、国内的重要学术期刊杂志上发表论文90余篇，其中SCI70余篇，同时，主持和完成国家自然科学基金和上海市自然科学基金等各类科研项目10余项；现在正主持国家自然科学基金面上项目1项，参加国家自然科学基金面上项目2项。