报告题目：Global Regularity and Large-Time Behavior of 3D Navier-Stokes Equations for Compressible Viscous Heat-Conducting Fluids

时间：2021年6月8日16:00-17:00
地点：综合楼811室

报告摘要：This talk is concerned with the Cauchy problem of Navier-Stokes equations for compressible viscous heat-conductive fluids. For less regular data and weaker compatibility condition than those proposed in the previous works, we prove the existence of local-in-time solutions belonging to a larger class of functions in which the uniqueness can be shown to hold. The local solution is in fact a classical one away from the initial time, provided the initial density is regular. We also establish the global well-posedness of classical solutions with large oscillations and vacuum in the case when the initial total energy is suitably small. The exponential decay estimates of the global solutions are obtained.

个人简介：张剑文，男，厦门大学数学科学学院教授、博导、副院长。主要研究方向为流体力学中的非线性偏微分方程（组），在Navier-Stokes、MHD、Boussinesq方程的适定性、正则性、稳定性、长时间性质和小参数极限等问题中取得若干研究成果，发表在SIMA、IUMJ、M3AS、JDE、JNLS、Nonlinearity等期刊上。连续主持多项国家自然科学基金项目，曾作为主要参与人获福建省自然科学奖二等奖、国家教学成果奖二等奖、福建省教学成果特等奖。