# The Boltzmann equation with specular boundary condition in convex domains

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Donghyun Lee , UW-Madison
Fine Hall 322

We establish the global-wellposedness and stability of the Boltzmann equation with the specular reflection boundary condition in general smooth convex domains when an initial datum is close to the Maxwellian with or without a small external potential. In particular, we have completely solved the long standing open problem after an announcement of Shizuta and Asano in 1977.