学 术 报 告

报告题目: The Green tensor of Stokes system in R_+^n

报告人: 赖柏顺（河南大学）
报告地点: 数学与统计学院 307
报告时间: 2020年11月24日下午3:00到5:00

数学与统计学院

2020.11.23

报告摘要：We prove the first ever pointwise estimates of the (unrestricted) Green tensor and the associated pressure tensor of the nonstationary Stokes system in the half-space, for every space dimension greater than one. The force field is not necessarily assumed to be solenoidal. The key is to find a suitable Green tensor formula which maximizes the tangential decay, showing in particular the integrability of Green tensor derivatives. With its pointwise estimates, we show the symmetry of the Green tensor, which in turn improves pointwise estimates. We also study how the solutions converge to the initial data, and the (infinitely many) restricted Green tensors acting on solenoidal vector fields. As applications, we give new proofs of existence of mild solutions of the Navier-Stokes equations in L^q, pointwise decay, and uniformly local L^q spaces in the half-space. This is a joint work with Kyungkeun Kang, Chen-Chih Lai and Tai-Peng Tsai.

报告人简介: 赖柏顺，河南大学数学学院教授、博导。主要研究方向为偏微分方程. 在Adv.math., SIAM J. Math. Anal.，Nonlinearity以及  J. Differential Equations等期刊发表SCI论文近30篇, 主持国家自然科学基金项目3项。