报告人：赖柏顺（河南大学）

报告人简介：赖柏顺，现为河南大学教授，博士生导师，长期从事非线性偏微分方程的理论研究，其研究领域包括不可压缩Navier-Stokes方程自相似解的存在性和唯一性，弱解正则性；椭圆方程解的渐近性态、稳定性、解集的分支现象、正则性。在国际刊物上发表SCI论文30余篇，主持国家课题青年基金、面上项目各一项; 主持河南省教育厅基金一项、河南大学优秀青年基金培育项目一项。其主要研究成果发表在 Advances in Mathematics, SIAM J. Math. Anal, Nonlinearity, Calc. Var. Partial Differential Equations, J. Differential Equations, Ann. Henri Poincare, Math. Res. Lett, Proc. Roy. Soc. Edinburgh Sect. A等重要的国际数学期刊上。

报告摘要：I will introduce two recent results in this talk on some fine properties of Green tensor of Stokes system. First, I will give an alternative proof of cancel property of Green tensor  of Stokes system in $\mathbb{R}^n$, which is more simple and direct. As an important application, we obtain the optimal decay estimate of forward self-similar solutions of the 3D incompressible Navier-Stokes Equations, constructed by Korobkov-Tsai. This work is the subsequence to our  recent work in [Advance in math 352 (2019), 981-1043].  Secondly, I sketch our another recent result about the the pointwise estimates of the Green tensor for the Stokes system in the half-space $\mathbb{R}_+^n$. In contrast to the Solonnikov's work, the external force needs not be divergence free. These estimates allow us to show the symmetry of the Green tensor and to construct mild solutions of the Navier-Stokes equations in uniform local Lq in the half space. The first work is joint with Changxing Miao and Xiaoxin Zheng, and the second is joint with Kyungkeun Kang, Chen-Chih Lai and Tai-Peng Tsai.

报告时间：2020年11月13日下午16：00-17:00

报告地点：育才校区数学楼205会议室

          欢迎感兴趣的老师和同学们参加！