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| Convergence Rate to Stationary Solutions for Boltzmann Equation with External Force |
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Citation： |
Seiji UKAI,Tong YANG,Huijiang ZHAO.Convergence Rate to Stationary Solutions for Boltzmann Equation with External Force[J].Chinese Annals of Mathematics B,2006,27(4):363~378 |
| Page view： 1205
Net amount： 945 |
Authors： |
Seiji UKAI; Tong YANG;Huijiang ZHAO |
Foundation： |
Project supported by the Grant-in-Aid for Scientific Research (C) (No.136470207), the Japan Society for the
Promotion of Science (JSPS), the Strategic Research Grant of City University of Hong Kong (No.7001608)
and the National Natural Science Foundation of China (No.10431060, No.10329101). |
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| Abstract： |
For the Boltzmann equation with an external force in the form of
the gradient of a potential function in space variable, the
stability of its stationary solutions as local Maxwellians was
studied by S. Ukai et al. (2005) through the energy method. Based
on this stability analysis and some techniques on analyzing the
convergence rates to stationary solutions for the compressible
Navier-Stokes equations, in this paper, we study the convergence
rate to the above stationary solutions for the Boltzmann equation
which is a fundamental equation in statistical physics for
non-equilibrium rarefied gas. By combining the dissipation from
the viscosity and heat conductivity on the fluid components and
the dissipation on the non-fluid component through the celebrated
H-theorem, a convergence rate of the same order as the one for the
compressible Navier-Stokes is obtained by constructing some energy
functionals. |
Keywords： |
Convergence rate, Boltzmann equation with external force, Energy functionals, Stationary solutions |
Classification： |
76P05, 35B35, 35F20 |
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