偏微分方程系列报告(朱长江教授、刘正荣教授和温焕尧教授)

发布时间:2019-04-09

朱长江教授学术报告

报告题目:Global classical solutions to compressible Navier-Stokes equations with vacuum

报 告 人:朱长江教授(华南理工大学)

报告时间:2019412(周五)上午9:00-9:50

报告地点:磬苑校区数学科学学院H306

报告摘要:In this talk, we will introduce the progress about the global classical solution of compressible Navier-stokes equations with vacuum, which includes the results on cases of one dimension, spherical symmetry in multi-dimensions, and multi-dimensions.This is a joint work with Huanyao Wen.

  

刘正荣教授学术报告

报告题目:BB方程的整体适定性及大时间行为

报 告 人:刘正荣教授(华南理工大学)

报告时间:2019412(周五)上午9:50-10:40

报告地点:磬苑校区数学科学学院H306

报告摘要:研究Boussinesq-Burgers方程的整体适定性及大时间行为。首先,基于合适的Dirichlet动态边界条件,证明了初值问题的整体存在性以及该解收敛到边值。其次,在一维空间中,证明了大初值解的整体存在性以及该解以代数衰减率收敛到常平衡态。

  

温焕尧教授学术报告

报告题目:Decay estimates of solutions to the incompressible Oldroyd-B model in R^3

报 告 人:温焕尧教授(华南理工大学)

报告时间:2019412(周五)上午10:40-11:30

报告地点:磬苑校区数学科学学院H306

报告摘要:We consider the Cauchy problem forthe 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.

  

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