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Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities

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Abstract

The hydrodynamic limit for the Boltzmann equation is studied in the case when the limit system, that is, the system of Euler equations contains contact discontinuities. When suitable initial data is chosen to avoid the initial layer, we prove that there exist a family of solutions to the Boltzmann equation globally in time for small Knudsen number. And this family of solutions converge to the local Maxwellian defined by the contact discontinuity of the Euler equations uniformly away from the discontinuity as the Knudsen number ε tends to zero. The proof is obtained by an appropriately chosen scaling and the energy method through the micro-macro decomposition.

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Authors and Affiliations

  1. Institute of Applied Mathematics, AMSS, Academia Sinica, China

    Feimin Huang & Yi Wang

  2. Department of Mathematics, City University of HongKong, Kowloon, HongKong

    Tong Yang

Authors
  1. Feimin Huang
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  2. Yi Wang
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  3. Tong Yang
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Correspondence to Feimin Huang.

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Communicated by H. Spohn

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Huang, F., Wang, Y. & Yang, T. Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities. Commun. Math. Phys. 295, 293–326 (2010). https://doi.org/10.1007/s00220-009-0966-2

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  • DOI: https://doi.org/10.1007/s00220-009-0966-2

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