信息科学技术学院/网络空间安全学院数学系学术讲座(十一)

发布单位:科学技术研究处 [2017-05-19 14:53:46] 打印此信息

题  目:On the Navier-Stokes equations in scaling-invariant spaces in any dimension

内容简介:Whether the solution to the systems of equations in fluid mechanics, such as those of Navier-Stokes and the magneto-hydrodynamics, remain smooth for all time in a three-dimensional space remains a challenging open problem. In 1962 Serrin provided a certain space-time integrability condition for smoothness in a scaling-invariant norms for the weak solution to the Navier-Stokes system, which is a three-dimensional velocity vector field. We discuss recent developments in the research direction in effort to improve such integrability conditions so that we only have to impose the condition on ``only one of the three'' velocity vector field components, instead of all of three, as well as its extension to the magneto-hydrodynamics system. The proof crucially relies on a key identity which is a consequence of the divergence-free property, and techniques from anisotropic Littlewood-Paley theory that consists of anisotropic Bernstein's inequality, anisotropic Bony paraproducts and anisotropic Besov and Sobolev spaces. Moreover, except only a very few recent results by the speaker, all such results have been limited to the three-dimensional case; we will also discuss the difficulty of extending to dimension such as four and beyond.

报告人:美国罗切斯特大学(University of Rochester)  Kazuo Yamazaki 教授

报告人简介:Kazuo Yamazaki received his Ph.D. in Mathematics from Oklahoma State University under the advisory of Prof. Jiahong Wu. Now he is a Professor at University of Rochester  His research direction is fluid dynamics PDE using harmonic and stochastic analysis, and mathematical biology and have published 35 papers.

时  间:2017年5月21日(周日)上午11:00始

地  点:南海楼3楼数学系会议室

 

热烈欢迎广大师生参加!

 

 

信息科学技术学院/网络空间安全学院

2017年5月19日