Global existence and stability of mild solutions to the Boltzmann system for gas mixtures

Ha, Seung-Yeal; Noh, Se; Yun, Seok

doi:10.1090/S0033-569X-07-01068-6

Authors: Seung-Yeal Ha, Se Eun Noh and Seok Bae Yun
Journal: Quart. Appl. Math. 65 (2007), 757-779
MSC (2000): Primary 35Q40
DOI: https://doi.org/10.1090/S0033-569X-07-01068-6
Published electronically: August 28, 2007
MathSciNet review: 2370359
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Abstract: We present the global existence and stability of mild solutions to the Boltzmann system with inverse power molecular interactions for a binary gas mixture, when initial data are sufficiently small and decay exponentially in phase space. For the existence and stability of mild solutions, we employ a modified Kaniel-Shinbrot’s scheme and a weighted nonlinear functional approach. Time-asymptotic convergence toward the free molecular motion is established using a weighted collision potential, and we show that the weighted $L^1$-distance between two mild solutions is uniformly controlled by that of initial data.

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