The Boltzmann equation near a rotational local Maxwellian

In rotationally symmetric domains, the Boltzmann equation with specular reflection boundary condition has a special type of equilibrium state called the rotational local Maxwellian which, unlike the uniform Maxwellian, has an additional term related to the angular momentum of the gas. In this paper, we consider the initial boundary value problem of the Boltzmann equation near the rotational local Maxwellian. Based on the L ²-L ^∞ framework of [Y. Guo, Arch. Ration. Mech. Anal., 197 (2010), pp. 713-809], we establish the global well-posedness and the convergence toward such equilibrium states.