廣西師范大學數學與統計學院
地址：廣西桂林市育才路15號 電話：0773—5846489（育才） 0773—5802163（雁山） 網站：www.95553544.buzz 郵箱：mathoff@gxnu.edu.cn
紀委郵箱：stxyjw@gxnu.edu.cn
報告人：賴柏順（河南大學）
報告人簡介：賴柏順，現為河南大學教授，博士生導師，長期從事非線性偏微分方程的理論研究，其研究領域包括不可壓縮Navier-Stokes方程自相似解的存在性和唯一性，弱解正則性；橢圓方程解的漸近性態、穩定性、解集的分支現象、正則性。在國際刊物上發表SCI論文30余篇，主持國家課題青年基金、面上項目各一項; 主持河南省教育廳基金一項、河南大學優秀青年基金培育項目一項。其主要研究成果發表在 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等重要的國際數學期刊上。
報告摘要：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.
報告時間：2020年11月13日下午16：00-17:00
報告地點：育才校區數學樓205會議室
歡迎感興趣的老師和同學們參加！
