報告題目：Decay estimates of solutions to the incompressible Oldroyd-B model in R^3

報 告 人：溫煥堯 教授（華南理工大學）

報告时间：2019年6月17日（星期一）上午10：30

報告所在：清水河校区主楼A1-513

邀 請 人：向昭銀 教授

報告摘要: 

We consider the Cauchy problem for  the incompressible Oldroyd-B model in R^3. For the case a=0, global existence results for weak solutions were derived by Lions and Masmoudi, allowing the initial data to be arbitrarily large, whereas it  is not known whether this assertion is true also for a which is not zero. We obtain time decay estimates for weak solutions subject  to arbitrary large data are given for  the case a=0. Furthermore, time-decay estimates are also given for strong solutions for  a which is not zero, however, for small initial data. The decay estimates obtained  are of the form that the k^{th} order derivatives in L^2 decay as (1+t)^{-\fr{3}{4}-\frac{k}{2}} for k=0,1,2 as t goes to infinity.Note that the coupling constant w does  not need to be small. This talk is based on the joint work with Matthias Hieber, and Ruizhao Zi.

報告人简介：

溫煥堯，男，華南理工大學數學學院教授、博士生導師、副院長。主要從事流體力學中的偏微分方程的數學理論研究。研究结果發表在Adv. Math.、Arch. Rational Mech. Anal.、J. Differential Equations、J. Functional Analysis、J.  Math. Pures Appl.、 Math. Models Meth. Appl. Sci.、SIAM J. Math. Anal.等雜志。先後主持中國博士後科學基金面上項目、特別資助項目，國家自然科學基金青年項目、面上項目和優秀青年科學基金項目。2016年獲廣東省青年珠江學者。