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Global Weak Solutions of the Boltzmann Equation

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Abstract

A new definition of the concept of weak solution of the nonlinear Boltzmann equation is introduced. It is proved that, without any truncation on the collision kernel, the Boltzmann equation in the one-dimensional case has a global weak solution in this sense. Global conservation of energy follows.

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Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Piazza L. da Vinci 32, 20133, Milano, Italy

    Carlo Cercignani

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  1. Carlo Cercignani
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Correspondence to Carlo Cercignani.

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Cercignani, C. Global Weak Solutions of the Boltzmann Equation. J Stat Phys 118, 333–342 (2005). https://doi.org/10.1007/s10955-004-8786-4

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  • DOI: https://doi.org/10.1007/s10955-004-8786-4

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