中科院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：Haitao Wang (Shanghai Jiao Tong University)

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

时  间：2022.07.25（星期一）14:00-15:00

地  点：Zoom ID: 924 888 5804  Passcode: AMSS2022

https://us06web.zoom.us/j/9248885804?pwd=OXg2VDhBT0pxRkd1Z3RJS0NFMnRDdz09

摘  要：It was established recently by Liu-Yu (Comm. Pure Appl. Math. 75:223, 2022) a constructive existence theory of weak solutions 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 for BV conductivity 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. 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.