Global well-posedness of compressible Navier-Stokes equations with BV data

讲座时间 Datetime: 2022年6月18日，星期六， 14:00-15:30

地点 Venue: 腾讯线上会议：565-953-369

 主持人 Host：邵国宽

报告人 Speaker:王海涛 

单位 Affiliation:上海交通大学

报告摘要 Abstract:

It was established recently by Liu-Yu (Comm. Pure Appl. Math. 75:223, 2022) a constructive existence theory of weak solution to isentropic Navier-Stokes equations with initial data of small total variation. The key ingredient in their work is the pointwise structures of heat kernel with BV coefficient. In this talk, we will first review their result. Then we extend the well-posedness theory to the full Navier-Stokes system by refining the heat kernel estimates and proving certain regularity estimates. If time permits, we will also mention how to obtain the space-time pointwise estimate of the solutions for BV data. This talk is based on joint works with Shih-Hsien Yu and Xiongtao Zhang.