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

Diffusive limit of Boltzmann Equation in exterior Domain