报告时间： 2023年11月30日15：00--16:00

报告地点：数统楼311会议室

报告题目：   Global Strong and Weak Solutions to the Initial-boundary-value Problem of 2D Compressible MHD System with Large Initial Data and Vacuum

报告人：施小丁（北京化工大学）

报告摘要：

  In this talk, we discuss the barotropic compressible magnetohydrodynamic equations with the shear viscosity being a positive constant and the bulk one being proportional to a power of the density in a general two-dimensional bounded simply connected domain. For initial density allowed to vanish, we prove that the initial-boundary-value problem of 2D compressible MHD system admits the global strong and weak solutions without any restrictions on the size of initial data provided the shear viscosity is a positive constant and bulk one is $\lambda=\rho^\beta$ with $\beta>4/3$. As we known, this is the first result concerning the global existence of strong solutions to the compressible MHD system in general two-dimensional bounded domains with large initial data and vacuum.

报告人简介：

  施小丁，北京化工大学教授。博士毕业于中国科学院数学与系统科学研究院，曾在日本大阪大学从事博士后研究。主要研究流体力学方程，包括可压缩Navier-Stokes方程组的冲击波、稀疏波、接触间断和边界层以及各种波的叠加、碰撞的大时间行为。非牛顿不可压缩Navier-Stokes方程组固液耦合问题和混合边值问题解的存在性、稳定性及数值分析。两相流Navier-Stokes-Cahn-Hilliard方程组、Navier-Stokes-Allen-Cahn方程组的解的适定性、大时间行为以及扩散界面极限问题等。部分成果发表在数学领域著名杂志Comm. Math. Phys., SIAM J. Math. Anal., Indiana Univ. Math. J., Nonlinearity，J. Differential Equations.等。多次主持国家自然科学基金项目。