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L 1 Stability of Multi-Dimensional Discrete-Velocity Boltzmann Equations

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Abstract.

We study the L 1 stability of multi-dimensional discrete-velocity Boltzmann equations. Under suitable smallness assumption on initial data, we show that bounded mild solutions are L 1 stable. For a stability estimate, we employ Bony’s multi-dimensional analysis for total interactions over characteristic planes.

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  1. Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, WI, 53706

    Seung-Yeal Ha

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  1. Seung-Yeal Ha
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Correspondence to Seung-Yeal Ha.

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Communicated by C. M. Dafermos

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Ha, SY. L 1 Stability of Multi-Dimensional Discrete-Velocity Boltzmann Equations. Arch. Rational Mech. Anal. 171, 25–42 (2004). https://doi.org/10.1007/s00205-003-0279-0

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