当前位置: 首页  学术动态

数学学科现代分析及其应用研究所学术报告(赖柏顺 河南大学)

发布者:付慧娟   发布时间:2021-01-18  浏览次数:10

报告题目:The Green tensor of the nonstationary Stokes system in the half space

报 告 人:赖柏顺教授河南大学

报告时间:2021年1月19日(星期二)19:30-20:30

报告地点:腾讯会议 ID:715 643 984

https://meeting.tencent.com/s/pWTVIz3QPz4G

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 direct 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. (In the subsequent work, we (with Kang-Lai-Tsai) will use it to construct a flow u with unbounded normal derivative in a region E near the boundary) This is a joint work with Kyungkeun Kang, Chen-Chih Lai, Tai-Peng Tsai

个人简介:赖柏顺,1981年1月生,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;四阶椭圆型方程极限解的正则性等. 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, Proc. Edinb. Math. Soc., Proc. Amer. Math. Soc., Discrete Contin. Dyn. Syst.等重要的国际数学期刊上。

邀请人:非线性泛函分析与偏微分方程团队

欢迎感兴趣的老师和同学参加!