Blow-up Solutions to a Viscoelastic Fluid System and a Coupled Navier–Stokes/Phase-Field System in <em>R</em><sup>2</sup>

doi:10.1088/0256-307X/28/6/060206

Chin. Phys. Lett.

2011, Vol. 28

Issue (6): 060206 DOI: 10.1088/0256-307X/28/6/060206

GENERAL

Blow-up Solutions to a Viscoelastic Fluid System and a Coupled Navier–Stokes/Phase-Field System in R²

ZHAO Li-Yun¹, GUO Bo-Ling², HUANG Hai-Yang^1**

¹School of Mathematical Sciences and Key Laboratory of Mathematics and Complex Systems (Ministry of Education), Beijing Normal University, Beijing 100875
²Nonlinear Center for Studies, Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088

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ZHAO Li-Yun, GUO Bo-Ling, HUANG Hai-Yang 2011 Chin. Phys. Lett. 28 060206

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Abstract The explicit solutions to both the Oldroyd-B model with an infinite Weissenberg number and the coupled Navier–Stokes/phase-field system are constructed by the method of separation of variables. It is found that the solutions blow up in finite time.

Keywords: 02.30.Gp 02.30.Jr

Received: 21 February 2011 Published: 29 May 2011

PACS:	02.30.Gp	(Special functions)
	02.30.Jr	(Partial differential equations)

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https://cpl.iphy.ac.cn/10.1088/0256-307X/28/6/060206 OR https://cpl.iphy.ac.cn/Y2011/V28/I6/060206

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	ZHAO Li-Yun
	GUO Bo-Ling
	HUANG Hai-Yang

[1] Lin F H, Liu C and Zhang P 2005 Commun. Pure Appl. Math. 58 1
[2] Lei Z, Liu C and Zhou Y 2008 Arch. Rational. Mech. Anal. 188 371
[3] Jacqmin D 1999 J. Comput. Phys. 155 96
[4] Liu C and Shen J 2003 Physica D 179 211
[5] Zhao L Y, Wu H and Huang H Y 2009 Commun. Math. Sci. 7 939
[6] Guo B L, Yang G S and Pu X K 2008 Chin. Phys. Lett. 25 2115

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