Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities

Details Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities

2009-04-12

arxiv.org/abs/0904.1836v1

Mathematics

Analysis of PDEs

34 pages. submitted

Scientific paper

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 exists a unique solution to the Boltzmann equation globally in time for any given 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 $\varepsilon$ 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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