美高梅手机登录网站,美高梅在线登录网址

网站建议北大主页ENGLISH旧版回顾

国际合作与交流

美高梅手机登录网站» 国际合作与交流» 国际学术交流» 国际学术活动的组织
MENU

【学术报告】Recent Progress on Singularity Formation of 3D Euler Equations and Related Models

报告人:Prof. Thomas Y. Hou(California Institute of Technology)

 

时   间:2019-06-28     15:00-16:00

 

地   点:理科1号楼1114室

 

Abstract: Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. We first review the numerical evidence of finite time singularity for 3D axisymmetric Euler equations by Luo and Hou. The singularity is a ring like singularity that occurs at a stagnation point in the symmetry plane located at the boundary of the cylinder. We then present a novel method of analysis and prove that the 1D HL model develops finite time self-similar singularity. We also apply this method of analysis to prove finite time self-similar blowup of the original De Gregorio model for some smooth initial data on the real line with compact support.  Self-similar blowup results for the generalized De Gregorio model for the entire range of parameter on the real line or on a circle have been obtained for Holder continuous initial data with compact support. Finally, we report our recent progress in analyzing the finite time singularity of the axisymmetric 3D Euler equations with initial data considered by Luo and Hou.

TOP
XML 地图 | Sitemap 地图