【加拿大McGill大学】Global and blow-up solutions for 1D compressible Euler equations with

2019年06月10日 09:47  点击：[]

报告题目Global and blow-up solutions for  1D compressible Euler equations with time-dependent damping

报告人：梅茗教授 (加拿大McGill大学及Champlain学院)

报告时间2019.06.14   下午15:30-16:30

报告地点：创新园大厦B1410

校内联系人：曹杨

报告摘要This talk deals with the Cauchy problem for the 1D compressible Euler

equations with time-dependent damping, where the time-vanishing damping in the like form of $\frac{\mu}{(1+t)^\lambda}$ makes the variety of the  dynamic system. For $0<\lambda<1$ and $\mu>0$, or $\lambda=1$ but $\mu>2$, where $\lambda=1$ and $\mu=2$ is the critical case, when the derivatives of the initial data are small, but the initial data themselves are allowed to be arbitrarily large, the solutions are proved to exist globally in time; while, when   the derivatives of the initial data are large at some points, then the solutions are still bounded, but their derivatives will blow up at finite time. For $\lambda=1$ and $0<\mu<1$, the derivatives of solutions will blow up for all initial data, including the small initial data. In order to prove the global existence of the solutions with large initial data, we introduce a new energy functional, which crucially helps to build up the maximum principle for the corresponding Riemann invariants, and the uniform boundedness for the local solutions, these keys finally guarantee the global existence of the solutions. The results presented here essentially improve and develop the existing studies.   Finally,  some numerical simulations in different cases are carried out, which further confirm our theoretical results. This is a joint work with Shaohua Chen, Haitong Li, Jingyu Li, and Kaijun Zhang.

报告人简介梅茗教授,自2005年起为加拿大McGill大学兼职教授及Champlain学院的终身教授，博士导师。意大利L’Aquila大学客座教授。2015年被聘为吉林省长白山学者讲座教授，东北师范大学“东师学者”讲座教授。主要从事流体力学中偏微分方程和生物数学中带时滞反应扩散方程研究，在ARMA, SIAM, JDE, Commun.PDEs等刊物发发表论文90多篇，是4家SCI国际数学杂志的编委并一直承担加拿大自然科学基金项目，魁北克省自然科学基金项目，及魁北克省大专院校国际局的基金项目。

数学科学学院

2019年6月10日

关闭