On the solvability and asymptotics of the Boltzmann equation in irregular domains.

Journal article, 1997

The paper considers the Boltzmann equation in irregular domains with finite Hausdorff measure of the boundary and a cone condition. The boundary interaction is of diffuse reflection type with constanc temperature on the boundary. The main results obtained are existence in a DiPerna—Lions style, and strong convergence to equilibrium in L1 when time tends to infinity, for the Boltzmann equation with Maxwellian boundary conditions in a bounded measure sense.