Global existence of weak solutions to the three-dimensional Prandtl equations with a special structure

Cheng-Jie LIU; Ya-Guang WANG; Tong YANG

doi:10.3934/dcdss.2016082

Author(s)

Cheng-Jie LIU
Ya-Guang WANG
Tong YANG

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	2011-2029
Journal / Publication	Discrete and Continuous Dynamical Systems - Series S
Volume	9
Issue number	6
Publication status	Published - Dec 2016

Link(s)

DOI	DOI https://doi.org/10.3934/dcdss.2016082 Final Published version
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Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-84995595785&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(2917e00f-2b70-403c-b121-b2f4dfd9e952).html

Abstract

The global existence of weak solutions to the three space dimensional Prandtl equations is studied under some constraint on its structure. This is a continuation of our recent study on the local existence of classical solutions with the same structure condition. It reveals the sufficiency of the monotonicity condition on one component of the tangential velocity field and the favorable condition on pressure in the same direction that leads to global existence of weak solutions. This generalizes the result obtained by Xin-Zhang [14] on the two-dimensional Prandtl equations to the three-dimensional setting.

Research Area(s)

3D Prandtl equations, Favorable pressure, Global existence, Monotonic velocity field, Weak solutions

Citation Format(s)

[ RIS ] [ BibTeX ]

Global existence of weak solutions to the three-dimensional Prandtl equations with a special structure. / LIU, Cheng-Jie; WANG, Ya-Guang; YANG, Tong.

In: Discrete and Continuous Dynamical Systems - Series S, Vol. 9, No. 6, 12.2016, p. 2011-2029.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

LIU, C-J, WANG, Y-G & YANG, T 2016, 'Global existence of weak solutions to the three-dimensional Prandtl equations with a special structure', Discrete and Continuous Dynamical Systems - Series S, vol. 9, no. 6, pp. 2011-2029. https://doi.org/10.3934/dcdss.2016082

LIU, C-J., WANG, Y-G., & YANG, T. (2016). Global existence of weak solutions to the three-dimensional Prandtl equations with a special structure. Discrete and Continuous Dynamical Systems - Series S, 9(6), 2011-2029. https://doi.org/10.3934/dcdss.2016082

LIU C-J, WANG Y-G, YANG T. Global existence of weak solutions to the three-dimensional Prandtl equations with a special structure. Discrete and Continuous Dynamical Systems - Series S. 2016 Dec;9(6):2011-2029. doi: 10.3934/dcdss.2016082

LIU, Cheng-Jie ; WANG, Ya-Guang ; YANG, Tong. / Global existence of weak solutions to the three-dimensional Prandtl equations with a special structure. In: Discrete and Continuous Dynamical Systems - Series S. 2016 ; Vol. 9, No. 6. pp. 2011-2029.