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| In this talk I will present two results on the Navier-Stokes-Fourier (NSF) limit from Boltzmann equation. The first is joint work with Masmoudi, in a bounded domain, we justify NSF with Dirichlet and Nuemann boundary condition from Boltzmann equation with Maxwell reflection boundary condition. The boundary conditions of NSF depends on the relative size of accommodation coefficient and Knudsen number. Moreover, by analyzing the viscous and kinetic boundary layers, we prove the strong L^1 convergence for Dirichlet condition. The second is joint work with Chao-jiang Xu and Hui-jiang Zhao, in the whole space, we prove the global classical solutions around the equilibrium uniform in Knudsen number for non-cutoff kernel Boltzmann equation, then taking fluid limit, then give a kinetic proof of the classical solutions of NSF around the equilibrium. |
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