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Weak Solutions of the Boltzmann Equation Without Angle Cutoff

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Abstract

The definition of the concept of weak solution of the nonlinear Boltzmann equation, recently introduced by the author, is used to prove that, without any cutoff in the collision kernel, the Boltzmann equation for Maxwell molecules 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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Cercignani, C. Weak Solutions of the Boltzmann Equation Without Angle Cutoff. J Stat Phys 123, 753–762 (2006). https://doi.org/10.1007/s10955-006-9115-x

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  • DOI: https://doi.org/10.1007/s10955-006-9115-x

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