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Energy method for Boltzmann equation

✍ Scribed by Tai-Ping Liu; Tong Yang; Shih-Hsien Yu

Book ID
104085747
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
161 KB
Volume
188
Category
Article
ISSN
0167-2789

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✦ Synopsis

A basic, simple energy method for the Boltzmann equation is presented here. It is based on a new macro-micro decomposition of the Boltzmann equation as well as the H-theorem. This allows us to make use of the ideas from hyperbolic conservation laws and viscous conservation laws to yield the direct energy method. As an illustration, we apply the method for the study of the time-asymptotic, nonlinear stability of the global Maxwellian states. Previous energy method, starting with Grad and finishing with Ukai, involves the spectral analysis and regularity of collision operator through sophisticated weighted norms.

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