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The Green tensor of Stokes system in R_+^n

发布时间：2020-11-23 作者： 浏览次数：
Speaker: 赖柏顺 DateTime: 2020年11月26日（周四）上午9:00-10:00
Brief Introduction to Speaker:

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。其主要研究成果发表在 Advances in Mathematics, Siam J. Math. Anal, Nonlinearity, Calc. Var. Partial Differential Equations 等国际刊物上。

 

 Place: 腾讯会议（会议号请联系王春花老师索取）
Abstract: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.
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