当前位置: 首页  学术动态

现代分析及其应用研究所学术报告(王勇 中国科学院数学与系统科学研究院)

发布者:数学与计算机科学学院   发布时间:2020-07-01  浏览次数:112

报告题目:Global Solutions of the Compressible Euler Equations with Large Initial Data of Spherical Symmetry and Positive Far-Field Density

人:王勇 副研究员(中国科学院数学与系统科学研究院)

报告时间:202072日(周四)10:00-11:00

报告地点:腾讯会议号116 759 448或添加至会议列表:https://meeting.tencent.com/s/tmAngYhJH7ie

 

摘要:We are concerned with the global existence theory for spherically symmetric solutions of the multidimensional compressible Euler equations with large initial data of positive far-field density so that the total initial-energy is {\it unbounded}. The central feature of the solutions is the strengthening of waves as they move radially inward toward the origin. For the large initial data of positive far-field density, various examples have shown that the spherically symmetric solutions of the Euler equations blow up near the origin at certain time. A fundamental unsolved problem is whether the density of the global solution would form concentration to become a measure near the origin for the case when the total initial-energy is unbounded. Another longstanding problem is whether a {\it rigorous proof} could be provided for the inviscid limit of the multidimensional compressible Navier-Stokes to Euler equations with large initial data.

In this paper, we establish a global existence theory for spherically symmetric solutions of the compressible Euler equations with large initial data of positive far-field density and relative finite-energy. This is achieved by developing a new approach via adapting a class of degenerate density-dependent viscosity terms, so that a rigorous proof of the vanishing viscosity limit of global weak solutions of the Navier-Stokes equations with the density-dependent viscosity terms to the corresponding global solution of the Euler equations with large initial data of spherical symmetry and positive far-field density can be obtained. One of our main observations is that the adapted class of degenerate density-dependent viscosity terms not only includes the viscosity terms for the Navier-Stokes equations for shallow water (Saint Venant) flows but also, more importantly, is suitable to achieve our key objective of this paper. These results indicate that concentration is not formed in the vanishing viscosity limit even when the total initial-energy is unbounded, though the density may blow up near the origin at certain time. This talk is based on a joint work with G. Q. Chen.


邀请人:姜在红

欢迎广大师生参加!