报告题目：Sharp decay estimates for Oldroyd-B model with only fractional stress tensor diffusion
报告人：许孝精 教授（北京师范大学）
报告时间：2022年7月8日（周五）下午15:00—18:00
腾讯会议ID：684 146 019
报告摘要：Precise large-time behavior of physical quantities plays a crucial role in understanding many physical phenomena. For partial differential equation (PDE) models with full dissipation, powerful methods such as the Fourier-splitting technique have been developed. However, these methods may not apply to PDE systems with only partial dissipation. In this talk, I shall offer new ideas on how to obtain precise large-time decay estimates on a partially dissipated system. We examine the $d$-dimensional incompressible Oldroyd-B model without velocity dissipation and with only fractional diffusive stress. The discovery here is that the coupling and interaction of the velocity and the non-Newtonian stress actually enhances the regularity and the stability of the system. Without the stress, the Sobolev norms of the velocity could grow rather rapidly in time, let alone decay at explicit rates. Making use of the interaction, we deduce a system of damped wave equations obeyed by the velocity and the Leray projection of the divergence of the stress. By constructing a suitable Lyapunov functional, we are able to control the growth in the derivatives and extract explicit decay rates. The optimal decay rates are established by representing the wave equations in an integral form and applying a bootstrapping argument. This is based on the joint work with Peixin Wang, Jiahong Wu, Yueyuan Zhong.
报告人简介：许孝精，男，北京师范大学数学科学学院教授，副经理。2005年于吉林大学获博士学位。主要研究流体动力学中偏微分方程组的适定性理论。博士学位论文获“吉林省优秀博士学位论文”。主持完成省部级及以上的科研项目多项。发表学术论文60余篇，部分结果发表在J. Math. Pures Appl., JFA，SIAM J. Math. Anal.，IUMJ，Nonlinearity，J. Nonlinear Science，CVPDE，JDE等知名杂志上。曾在法国、美国、加拿大、波兰和香港等地区进行学术访问十余次。
