报告题目：Blowup of the entropy-bounded classical solutions to the nonisentropic compressible Navier-Stokes equations

报告人：袁源（华南师范大学）

报告时间：2023年12月5日15:00-16:00

报告地点：88038威尼斯323（腾讯会议932 495 5583）

邀请单位：88038威尼斯

报告内容简介：

This talk concerns the instantaneous blowup of entropy-bounded classical solutions to the vacuum free boundary problem and the Cauchy problem of nonisentropic compressible Navier-Stokes equations.

Vacuum free boundary problem: it is proved that with degenerate, temperature-dependent transport coefficients and prescribed decaying rate of the initial density across the vacuum boundary, (1) for three-dimensional spherically symmetric flows with non-vanishing bulk viscosity and zero heat conductivity, entropy-bounded classical solutions do not exist for any time, provided the initial velocity is expanding near the boundary; (2) for flows with non-vanishing heat conductivity, the normal derivative of the temperature of the classical solution across the free boundary does not degenerate, and therefore the entropy immediately blowups if the decaying rate of the initial density does not satisfy the physical vacuum condition;

Cauchy problem: we also have similar results for the one-dimensional flows with zero heat conduction and prescribed fast-decaying initial density profiles.

These are joint works with Professor Zhouping XIN from the Chinese University of Hong Kong, Professor Jinkai LI from South China Normal University and Dr. Xin LIU from Texas A&M University.

报告人简介：

袁源，华南师范大学数学科学学院副研究员。2018年博士毕业于香港中文大学，导师为辛周平教授。毕业至今在华南师范大学工作，其间于布雷西亚大学以博士后身份研修访问约一年，合作导师为Paolo Secchi教授。主要从事流体动力学方程方面的研究，包括磁流体自由界面问题、含真空的Navier-Stokes方程自由界面问题、守恒律方程的周期扰动问题等。目前已在JMPA、M3AS、IUMJ、SIMA、中国科学数学（SCM）等国际学术期刊上发表SCI论文9篇。