时间：2025年5月17日8:20

地点：东校区第二教学楼2106（学术报告厅）

报告人：张挺 浙江大学 教授        

报告摘要：

In this talk, we consider the three dimensional compressible viscoelastic flows with zero shear viscosity, and a general class of pressure laws. We do not need the monotonically increasing pressure law with the help of the elasticity coefficient $\theta$ of the fluid, only need the condition $P^\prime(1)+\theta>0$. We shall reformulate the systems with the new perturbation variables $(\rho-1,u,F-\frac{1}{\rho}I)$ and $(\rho-1,u,F-I)$ to deal with thecompressible and incompressible parts, separately. For the compressible parts,we shall use the vector fields methods to derive the weighted energy decay. Forthe incompressible parts, a local energy decay will be applied to derive the weighted estimates. To overcome the difficulty of the lack of dissipation for the incompressible parts, we shall introduce "good unknowns'', and use the implicit structure of the nonlinearities. With the help of vector fields, we derive the weighted $L^2$ energy to prove global stability around a constantequilibrium. (Based on joint work with Xianpeng Hu and Song Meng)

报告人简介：

张挺，浙江大学数学科学学院教授，博士生导师，美国普林斯顿大学访问学者。入选国家万人计划“首批青年拔尖人才支持计划”，教育部“新世纪优秀人才支持计划”，浙江省杰出青年科学基金项目获得者，浙江省“新世纪151人才工程”第二层次培养对象，获得教育部自然科学奖二等奖等荣誉。长期从事流体力学偏微分方程(组)的数学理论研究，主持多项国家自然科学基金项目和省部级项目，在可压缩与不可压缩Navier-Stokes方程组、MHD方程组、粘弹性流体力学方程组等方面取得系列重要研究成果，发表SCI 论文100 余篇。部分成果出版在《Comm.Math. Phys.》，《Arch. Rational Mech. Anal.》，《Math. Ann.》,《SIAM J. Math.Anal.》，《Int.Math. Res. Notices》等国际著名期刊上。