讲座题目：The Green tensor of the nonstationary Stokes system in the half space

讲座时间：2021年5月14日，星期五，下午2:40-4:00

讲座地点：数学楼2-2会议室

讲座人：赖柏顺教授，湖南师范大学

讲座摘要：

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 Lq, pointwise decay, and uniformly local Lq spaces in the half-space. We also show the existence of Navier-Stokes flows with finite global energy and unbounded velocity derivative near the boundary, caused by Holder continuous boundary fluxes with compact support. This talk is based on joint work with Kyungkeun Kang and Chen-Chih Lai, Tai-peng Tsai~(arXiv:2011.00134 and work in progress).

讲座人简介：

    赖柏顺，1981年1月生，现为湖南师范大学潇湘学者特聘教授，目前的主要研究领域为不可压缩Navier-Stokes方程的数学理论；在国际刊物上发表SCI论文30余篇，主持国家课题3项。其主要研究成果发表在 Transaction, AMS, Advances in Mathematics, Siam J. Math. Anal, Nonlinearity, Calc. Var. Partial Differential Equations, J. Differential Equations 等重要的国际数学期刊上。