# Hydrodynamic Limit of the Boltzmann Equation with Contact Discontinuities - Mathematics > Analysis of PDEs

Abstract: The hydrodynamic limit for the Boltzmann equation is studied in the case whenthe limit system, that is, the system of Euler equations contains contactdiscontinuities. When suitable initial data is chosen to avoid the initiallayer, we prove that there exists a unique solution to the Boltzmann equationglobally in time for any given Knudsen number. And this family of solutionsconverge to the local Maxwellian defined by the contact discontinuity of theEuler equations uniformly away from the discontinuity as the Knudsen number$\varepsilon$ tends to zero. The proof is obtained by an appropriately chosenscaling and the energy method through the micro-macro decomposition.

Author: Feimin Huang, Yi Wang, Tong Yang

Source: https://arxiv.org/