Japan Journal of Applied Mathematics

, Volume 7, Issue 2, pp 301-320

The Boltzmann equation and thirteen moments

  • Shuichi KawashimaAffiliated withDepartment of Applied Science, Faculty of Engineering 36, Kyushu University

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.

Key words

Boltzmann equation stability of Maxwellian energy method Ljapunov function thirteen moments