题目：Global and blow-up solutions for 1D compressible

Euler equations with time-dependent damping.

报告人：Prof. Ming Mei (梅茗教授)

加拿大Champlain College & McGill University

Abstract : 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; for these global solutions, we further technically determine what will be their corresponding asymptotic profiles, particularly in the critical case with /lambda=1, and then show the convergence with optimal rates; 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 series of 3 joint works with Shaohua Chen, Shifeng Geng, Haitong Li, Jingyu Li, Yanping Lin and Kaijun Zhang.

时间：2019年7月5日（星期五）

上午10:00-11:00

地点：565net必赢客户端本部教二楼527教室

联系人：牛冬娟

欢迎全体师生积极参加！