Solutions of the Cauchy problem for the Boltzmann equation with Grad's cutoff have a number of desirable properties (uniqueness, continuous dependence on the data, propagation of derivatives and moments...) provided a "strong" estimate, typically involving an L∞ norm of the macroscopic quantities holds. In problems with bounded domains, such estimates can be obtained either for short times, or in cases when the corresponding hydrodynamic solution is smooth. However, when the dependence on the spatial variable is one-dimensional there is more to the story, and in my talk I will discuss this case.
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