报告题目: A remark on the nonexistence of positive solution for a class of integral equation and its application

报告人：湖南农业大学理学院  许建开（副教授）

报告时间：12月12日下午14:00-15:30

报告地点：数计学院4号楼229会议室

摘要:In [J.Xu, H.Wu and Z. Tan,The non-existence results for a class of integral equation, J. Diff.equation. {\\bf256} (2014), 1873-1902], the authors consider thefollowing integral system

u(x,b)=\\int_{\\mathbb{R}^n} \\frac{u^q(y,b)}{(b+|x-y|)^{\\lambda}}dy

and under the technical restrictions $\\lambda\\in (0,~n-1/3)$ and$q=2n/\\lambda-1$, proved system $(\ef{eq0})$ doesn't have apositive solution in $L^{q+1}(\\mathbb{R}^n)(n>2)$. In this paper, werelax this assumption and show that as $\\lambda\\in (0,~n)$ and$q=2n/\\lambda-1$, system $(\ef{eq0})$ doesn't admit a positivesolution which is, beyond our intuitions,  essential different fromthe original conformal invariant integral system and simultaneouslyimplies that under some condition, the sharp constant of weak typeconvolution-Young's inequality with kernel function$h(x)=(b+|x|)^{-\\lambda}$ doesn't exist.

报告题目: Global existence of the finite energy weak solutions to a nematic liquid crystals model

报告人：湖南农业大学理学院  许建开（副教授）

报告时间：12月12日下午16:00-17:30

报告地点：数计学院4号楼229会议室

摘要:In this talk, we are concerned with a simplified hydrodynamic equation, proposed by Ericksen and Leslie, modelingthe flow of nematic liquid crystals. For a bounded domain in R3, under the assumption that initial density belongs to $L^{\\gamma}(\\Omega), \\gamma> 3/2$ we show the global existence of weak solutions to the nematic liquid crystals model with a penalized system. Furthermore, we also obtain the energy inequality for weak solutions.