Abstract
This report discusses a new approach for the resolution of the fluid-dynamic limit for the Broadwell system of the kinetic theory of gases, appropriate in the case of Riemann, Maxwellian data. Since the formal limiting system is expected to have self-similar solutions, we are motivated to replace the Knudsen number ɛ in the Broadwell model so that the resulting model admits self-similar solutions ξ=x/t and then let ɛ go to zero. The limiting procedure is justified and the resulting limit is a solution of the Riemann problem for the fluid-dynamic limit equations. A class of Riemann data for which this program can be carried out is exhibited. Furthermore, it is shown that for the Carleman model the complete program can be done successfully for arbitrary Riemann data.
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Communicated by T.-P. Liu
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Slemrod, M., Tzavaras, A.E. Self-similar fluid-dynamic limits for the Broadwell system. Arch. Rational Mech. Anal. 122, 353–392 (1993). https://doi.org/10.1007/BF00375140
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DOI: https://doi.org/10.1007/BF00375140