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数学家将会最终给出Navier-Stokes方程的解吗?
Alternative TitleWill mathematicians unleash the power of the Navier-Stokes equations?
张平
2018-01-01
Source Publication科学通报
ISSN0023-074X
Volume63.0Issue:012Pages:1082-1087
Abstract自1934年Leray证明不可压缩Navier-Stokes方程的整体有限能量分布弱解以来,关于三维Leray弱解的正则性和唯一性,以及是否存在有限能量爆破解的研究,一直是流体力学数学理论的核心课题之一.该问题和Clay研究所公布的七大千禧年问题之一——关于三维Navier-Stokes方程的整体正则性——紧密相关.本文主要介绍此问题以及该问题的相关研究进展.
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
Language中文
CSCD IDCSCD:6273148
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/53801
Collection中国科学院数学与系统科学研究院
Affiliation中国科学院数学与系统科学研究院
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.
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