Nonlinear stability of the Boltzmann equation in a periodic box
Kung-Chien Wu · Journal of Mathematical Physics · 2015
We study the nonlinear stability of the Boltzmann equation in the 3-dimensional periodic box with size 1/ε of each side, where 0 < ε ≪ 1 is the Knudsen number. The initial perturbation is not necessary smooth. The convergence rate is algebraic for small time region and exponential for large time region. Moreover, the algebraic rate is optimal and the exponential rate depends on the size of the domain (Knudsen number).