Exponential convergence to the Maxwell distribution for some class of Boltzmann equations
This paper concerns a class of nonlinear Boltzmann equations describing return to thermal equilibrium in a gas of colliding particles suspended in a thermal medium. It is proved that, in a three-dimensional flat torus, and for sufficiently small values of the mole number of the gas, the solutions with smooth initial datum in a weighted \(L^1\)-space converges to the global Maxwellian in an \(L^1\)-space, exponentially fast in time. The authors' argument mainly uses perturbation theory to prove decay estimates for propagators.
scientific article