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      Global bounded solutions to the Boltzmann equation for a polyatomic gas

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          Abstract

          In this paper we consider the Boltzmann equation modelling the motion of a polyatomic gas where the integration collision operator in comparison with the classical one involves an additional internal energy variable \(I\in\mathbb{R}_+\) and a parameter \(\delta\geq 2\) standing for the degree of freedom. In perturbation framework, we establish the global well-posedness for bounded mild solutions near global equilibria on torus. The proof is based on the \(L^2\cap L^\infty\) approach. Precisely, we first study the \(L^2\) decay property for the linearized equation, then use the iteration technique for the linear integral operator to get the linear weighted \(L^\infty\) decay, and in the end obtain \(L^\infty\) bounds as well as exponential time decay of solutions for the nonlinear problem with the help of the Duhamel's principle. Throughout the proof, we present a careful analysis for treating the extra effect of internal energy variable \(I\) and the parameter \(\delta\).

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          Journal
          11 October 2022
          Article
          2210.05191
          96790b77-c078-4dbc-9660-974a78c0c074

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          31 pages. All comments are welcome
          math.AP

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