Global Diffusive Expansion of Boltzmann Equation in exterior Domain

The study of flows over an obstacle is one of the fundamental problems in fluids. In this paper we establish the global validity of the diffusive limit for the Boltzmann equations to the Navier-Stokes-Fourier system in an exterior domain. To overcome the well-known difficulty of the lack of Poincare's inequality in unbounded domain, we develop a new $L^2-L^3-L^6$ splitting to extend $L^2-L^\infty$ framework into the unbounded domain.