Renormalization Group and Asymptotics of Solutions of Potential Flows
博士 === 國立成功大學 === 數學系 === 89 === The subject matter of this thesis is to apply the renormalization theory to study the asymptotic behaviour of some specific flows. There are two parts in this thesis. One is to use the renormalization group method developed by Chen, Goldenfeld a...
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| Format: | Others |
| Language: | en_US |
| Published: |
2001
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| Online Access: | http://ndltd.ncl.edu.tw/handle/06594021899054412257 |
| Summary: | 博士 === 國立成功大學 === 數學系 === 89 === The subject matter of this thesis is to apply the renormalization theory to study the asymptotic behaviour of some specific flows. There are two parts in this thesis.
One is to use the renormalization group method developed by Chen, Goldenfeld and Oono 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.
In the other one we study the turbulent diffusion of the KdV-Burgers and Kuramoto-Sivashinsky equations. Using the concept of renormalization we prove that the homogenized equation is the diffusion equation for short-range correlation while for long-range correlation is the superdiffusion equation.
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