报告题目：Entropy-bounded Solutions to the Compressible Navier-Stokes Equations with Far Field Vacuum

主 讲 人：李进开

单 位：华南师范大学

时 间：9月17日9:00

腾 讯 ID：845 810 263

摘 要：

The entropy is one of the fundamental physical states of a fluid. For the ideal gases, it can be expressed as a certain linear combination of the logarithms of the density and temperature in the non-vacuum region, and, in the viscous case, it satisfies an equation of highly singular in the region close to the vacuum. Due to the singularity of the logarithmic function at zero and the singularity of the entropy equation near the vacuum region, the mathematical analyses on the behavior of the entropy near the vacuum region, were rarely carried out; in particular, in the presence of vacuum, it was unknown if the entropy remains its boundedness. It will be shown in this talk that the ideal gases retain their uniform boundedness of the entropy, locally or globally in time, if the vacuum occurs at the far field only and the density decays slowly enough at the far field. Precisely, we consider the Cauchy problem to the full compressible Navier-Stokes equations, with or without heat conductivity, and establish the local and global existence and uniqueness of solutions with uniformly bounded entropy in space at each time slice, in the presence of vacuum at the far field only. These are joint works with Prof . Zhouping Xin.

简 介：

李进开，华南师范大学研究员，博士生导师，2018年入选“国家海外高层次人才引进计划”青年项目，曾获得“2020世界华人数学家联盟最佳论文奖”金奖（2020 ICCM Best Paper Award）以及“第二届中国科协优秀科技论文”奖。2013年博士毕业于香港中文大学数学科学研究所，导师为辛周平教授。2013至2016于以色列威兹曼科学研究所（Weizmann Institute of Sciences）从事博士后研究工作，合作导师为Edriss S. Titi教授。2016至2018在香港中文大学数学系任研究助理教授。2018年起至今在华南师范大学工作。主要从事流体动力学方程方面的研究，主要包括大气海洋动力学偏微分方程、Navier-Stokes方程组、复杂流体等。目前已在包括CPAM，Adv. Math，JFA， ARMA， CPDE，SIAM等国际学术期刊上发表SCI论文30余篇，主持国家自然科学基金面上项目1项，香港研究资助局面上项目1项，广东省基础与应用基础研究基金自然科学基金面上项目1项，广东省基础与应用基础研究基金粤港澳应用数学中心项目1项。