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L1 and BV-type stability of the inelastic Boltzmann equation near vacuum

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Abstract

The L 1 and BV-type stability to mild solutions of the inelastic Boltzmann equation is given in this paper. The result is an extension of the stability of the classical solution of the elastic Boltzmann equation proved in Ha (Arch. Ration. Mech. Anal. 173:25–42, 2004 [16]). The observation relies on the energy loss of the inelastic Boltzmann equation. This is a continuity work of Alonso (Indiana Univ. Math. J. [1]), where the author obtained the global existence of a mild solution for the inelastic Boltzmann equation. The proof is based on the mollification method and constructing some functionals as the one in Chae and Ha (Contin. Mech. Thermodyn. 17(7):511–524, 2006 [9]).

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  1. Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Zhigang Wu

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  1. Zhigang Wu
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Correspondence to Zhigang Wu.

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Communicated by H. Spohn.

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Wu, Z. L1 and BV-type stability of the inelastic Boltzmann equation near vacuum. Continuum Mech. Thermodyn. 22, 239–249 (2010). https://doi.org/10.1007/s00161-009-0127-z

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  • DOI: https://doi.org/10.1007/s00161-009-0127-z

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