Global solutions in $W_k^{\zeta ,p}{L}_T^{\infty }{L}_v^2$ for the Boltzmann equation without cutoff

Abstract

The Boltzmann equation without an angular cutoff in a three-dimensional periodic domain is considered. The global-in-time existence of solutions in a function space $W_k^{\zeta ,p}{L}_T^{\infty }{L}_v^2$ with $p>1$ and $\zeta >3(1-\frac{1}{p})$ is established in the perturbation framework and the long-time behavior of solutions is also obtained for both hard and soft potentials. The proof is based on several norm estimates.

arXiv comment21 pages