Alternative TitleWill mathematicians unleash the power of the Navier-Stokes equations?
Source Publication科学通报
Other AbstractSince 1934 when Leray proved the global existence of finite energy weak solutions to 3D incompressible Navier-Stokes equations,the regularity and uniqueness of Leray weak solutions has been core in the mathematical theory of incompressible fluid mechanics.This problem is also closely related to the Millionaire’s problem proposed by Clay Institute,namely,the global regularity or singularity to finite energy solutions of 3D incompressible Navier-Stokes system.The goal of this article is first to introduce the problem and then to survey some progresses on this problem.In Section 1,following Fefferman,we first present the Millionaire’s problem concerning 3D incompressible Navier-Stokes equations.We also present the result of Leray on the global existence of finite energy weak solutions to the system.We conclude the introduction by remarking that the reason why we cannot solve the global regularity of 3D Navier-Stokes is that the system is energy super-critical.Whereas the energy law is so far the only conservation law which we can find for 3D Navier-Stokes system.The goal of Section 2 is to present the main approaches toward the regularity of 3D Navier-Stokes system,namely,partial regularity of suitable weak solutions to 3D Navier-Stokes system,conditional regularity of Leray solutions,and well-posedness of 3D Navier-Stokes system with initial data in the critical spaces.Finally,in the last section,we comment about the possible singularity of 3D Navier-Stokes system.
KeywordNavier-Stokes方程 正则性 奇性解 适定性
Indexed ByCSCD
Citation statistics
Document Type期刊论文
Recommended Citation
GB/T 7714
张平. 数学家将会最终给出Navier-Stokes方程的解吗?[J]. 科学通报,2018,63.0(012):1082-1087.
APA 张平.(2018).数学家将会最终给出Navier-Stokes方程的解吗?.科学通报,63.0(012),1082-1087.
MLA 张平."数学家将会最终给出Navier-Stokes方程的解吗?".科学通报 63.0.012(2018):1082-1087.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[张平]'s Articles
Baidu academic
Similar articles in Baidu academic
[张平]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[张平]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.