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January  2004, 11(1): 161-188. doi: 10.3934/dcds.2004.11.161

Asymptotic behavior of the compressible viscous potential fluid: Renormalization group approach

Chiu-Ya Lan 1, and  Chi-Kun Lin 2,

1. 

Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan
2. 

Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan

Received  February 2003 Revised  January 2004 Published  April 2004

In this article we apply the renormalization group method to study the potential flows of a compressible viscous fluid at small Reynolds number. The derived renormalization equation of order one is a system of reaction convection diffusion equations. The global existence and uniqueness of the weak solutions satisfying the energy inequality are proved following the methodology of Leray. The comparison between the exact solution and its approximation is also discussed.
Keywords: Slight compressible potential flow, incompressible limit., renormalization group, reaction convection diffusion system, wave group.
Mathematics Subject Classification: 35K50, 35L5.
Citation: Chiu-Ya Lan, Chi-Kun Lin. Asymptotic behavior of the compressible viscous potential fluid: Renormalization group approach. Discrete & Continuous Dynamical Systems, 2004, 11 (1) : 161-188. doi: 10.3934/dcds.2004.11.161
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