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On Cauchy problems of thermal non-equilibrium flows with small data

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Abstract

We study the equations describing the motion of a thermal non-equilibrium gas with one non-equilibriummode. In three space dimensions it is a hyperbolic system of six equations with a relaxation term. The dissipation mechanism induced by the relaxation is weak in the sense that Shizuta-Kawashima criterion is violated. However, there is a significant difference between one dimensional and three dimensional flows in how the criterion is violated. As a consequence, the velocity components in their solutionsbehave differentlywhile thermal dynamic variables share common properties.

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Authors and Affiliations

  1. Department of Mathematics, University of Alabama at Birmingham, Birmingham, USA

    Yanni Zeng

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  1. Yanni Zeng
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Correspondence to Yanni Zeng.

Additional information

This work was partially supported by a grant from the Simons Foundation (#244905 to Yanni Zeng).

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Zeng, Y. On Cauchy problems of thermal non-equilibrium flows with small data. Bull Braz Math Soc, New Series 47, 799–809 (2016). https://doi.org/10.1007/s00574-016-0187-1

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  • DOI: https://doi.org/10.1007/s00574-016-0187-1

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