Local weak solution of the isentropic compressible Navier-Stokes equations
Huang, Xiangdi1; Yan, Wei2,3
AbstractWhether the three dimensional isentropic compressible Navier-Stokes equations admit weak solutions for arbitrary initial data with adiabatic exponent gamma > 1 remains a challenging problem. The only available results under gamma > 1 were achieved by either assuming the initial data with small energy due to Hoff [J. Differ. Equations 120(1), 215-254 (1995)] or under the spherically symmetric condition by Jiang and Zhang [Commun. Math. Phys. 215, 559-581 (2001)] and Huang [J. Differ. Equations 262, 1341-1358 (2017)]. In this paper, we establish the existence of weak solutions with higher regularity of the three-dimensional periodic compressible isentropic Navier-Stokes equations in small time for the adiabatic exponent gamma > 1 in the presence of vacuum. It can be viewed as a local version of Hoff's work and also extends the result of Desjardins [Commun. Partial Differ. Equations 22(5-6), 977-1008 (1997)] by removing the assumption of gamma > 3.

Indexed BySCI
Funding ProjectNational Natural Science Foundation of China[11871113] ; National Natural Science Foundation of China[11371064] ; K. C. Wong Education Foundation ; Youth Innovation Promotion Association CAS
WOS Research AreaPhysics
WOS SubjectPhysics, Mathematical
WOS IDWOS:000717530600002
PublisherAIP Publishing
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Document Type期刊论文
Corresponding AuthorHuang, Xiangdi
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing, Peoples R China
2.Inst Appl Phys & Computat Math, Lab Computat Phys, Beijing, Peoples R China
3.Chinese Acad Sci, Hua Loo Keng Key Lab Math, Beijing, Peoples R China
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GB/T 7714
Huang, Xiangdi,Yan, Wei. Local weak solution of the isentropic compressible Navier-Stokes equations[J]. JOURNAL OF MATHEMATICAL PHYSICS,2021,62(11):8.
APA Huang, Xiangdi,&Yan, Wei.(2021).Local weak solution of the isentropic compressible Navier-Stokes equations.JOURNAL OF MATHEMATICAL PHYSICS,62(11),8.
MLA Huang, Xiangdi,et al."Local weak solution of the isentropic compressible Navier-Stokes equations".JOURNAL OF MATHEMATICAL PHYSICS 62.11(2021):8.
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