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Boltzmann equation and heat conduction

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In the study of the heat transfer in the Boltzmann theory, the basic problem is to construct solutions to the steady problem for the Boltzmann equation in a general bounded domain with diffuse reflection boundary conditions corresponding to a non-isothermal temperature of the wall. We discuss about the recent development of theory to characterize such a solution mathematically. As an application of the theory combining with available numerical simulations, we predict the break-down of the Fourier law in the kinetic regime. This is a joint work with Esposito, Guo, Marra In the talk we will start from basic stuffs and the preprint is available in ARXIV ( ).

This talk is part of the Cambridge Analysts' Knowledge Exchange series.

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