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A uniform perturbative result for the Boltzmann equation

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Rarefied gas dynamics are governed by the Boltzmann equation that takes into account the average number of collisions per particle per unit of time. One can expect that as this number (the inverse of Knudsen number) tends to infinity, the dynamic will tend to one of the fluid dynamics model (acoustics, Euler, Navier-Stokes, Stokes). After giving a brief description of the Boltzmann equation and some properties satisfied by the Boltzmann operator in a perturbative setting, this talk will establish existence and decay results for perturbative solutions around a global Maxwellian, uniformly in the Knudsen number. Such uniform behaviour leads to the convergence of the Boltzmann equation towards the Incompressible Navier-Stokes equations in a perturbative setting.

This talk is part of the Cambridge Analysts' Knowledge Exchange (C.A.K.E.) series.

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