The last chapter of this survey is devoted to the compressible Euler limit, and is actually a series of remarks and open problems more than a compendium of results.
We will discuss some perspectives regarding the mathematical treatment of this asymptotics. Slight adaptations of the modulated entropy method presented in the previous chapter should give likewise the local convergence towards smooth solutions to the compressible Euler equations under some integrability assumption on the solutions to the Boltzmann equation.
We further hope that suitable improvements of the modulated entropy method (including the modulation of the entropy dissipation) should provide the global convergence of weak solutions to the Boltzmann equation towards entropic solutions to the Riemann problem in one space dimension. The main challenge is of course to understand how the entropy dissipation concentrates on shocks and discontinuities.
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© 2009 Springer-Verlag Berlin Heidelberg
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Saint-Raymond, L. (2009). The compressible Euler limit. In: Hydrodynamic Limits of the Boltzmann Equation. Lecture Notes in Mathematics(), vol 1971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92847-8_6
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DOI: https://doi.org/10.1007/978-3-540-92847-8_6
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