分野別セミナー

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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 tends to zero. Moreover, the
convergence rate with respect to the Knudsen number is
obtained. The proof is obtained by an appropriately chosen
scaling and the energy method through the micro-macro
decomposition.