Abstract
The initial value problem for the nonlinear Boltzmann equation is studied. For the existence of global solutions near a Maxwellian, it is important to obtain a desired decay estimate for the linearized equation. In previous works, such a decay estimate was obtained by a method based on the spectral theory for the linearized Boltzmann operator. The aim of this paper is to show the same decay estimate by a new method. Our method is the so-called energy method and makes use of a Ljapunov function for the ordinary differential equation obtained by taking the Fourier transform. Our Ljapunov function is constructed explicitly by using some property of the equations for thirteen moments.
| Original language | English |
|---|---|
| Pages (from-to) | 301-320 |
| Number of pages | 20 |
| Journal | Japan Journal of Applied Mathematics |
| Volume | 7 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 1990 Jun |
| Externally published | Yes |
Keywords
- Boltzmann equation
- Ljapunov function
- energy method
- stability of Maxwellian
- thirteen moments
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics