报告题目：Some well-posedness results for the multi-dimensional viscoelastic flows

报告人：浙江大学张挺教授

报告时间：2024年6月29日08:00-10:00

报告地点：数学与统计学院312

邀请单位：福州大学数学与统计学院，江飞，林雪云

报告内容简介：

In this talk, we mainly focus on the multi-dimensional viscoelastic flows of Oldroyd type. First, considering a system of equations related to the incompressible viscoelastic fluids of Oldroyd-B type, we obtain the existence and uniqueness of the global solution, and the pointwise estimates of solutions. Then, considering a system of equations related to the compressible viscoelastic fluids of Oldroyd-B type with the general pressure law, $P’(\bar{\rho})+\alpha>0$, with $\alpha>0$ being the elasticity coefficient of the fluid, we prove the global existence and uniqueness of the strong solution in the critical Besov spaces when the initial data $u_0$ and the low frequency part of $\rho_0$, $\tau_0$ are small enough compared to the viscosity coefficients. The proof we display here does not need any compatible conditions. In addition, we also obtain the optimal decay rates of the solution in the Besov spaces. At Last, considering the multi-dimensional compressible Oldroyd-B model, which is derived by Barrett, Lu, and Suli (Comm. Math. Sci. 2017) through the micro-macro analysis of the compressible Navier-Stokes-Fokker-Planck system in the case of Hookean bead-spring chains. We would provide a unified method to study the system with the background polymer number density $\eta_\infty\geq0$, including the vanishing case and the nonvanishing case, and establish the global-in-time existence of the strong solution for the associated Cauchy problem when the initial data are small in the critical Besov spaces.

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”第二层次培养人员，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而项目，在可压缩与不可压缩Navier-Stokes、MHD方程、粘弹性流体力学方程等取得系列重要研究成果，发表在《Commun. Math. Phys.》、《Arch. Rational Mech. Anal.》、《SIAM J. Math. Anal.》、《Int Math Res Notices》、《J. Differential Equations》等国际期刊,SCI文章一百多篇,H指数为28。