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-Yang1**
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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