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Recently linear dissipative models of the Boltzmann equation have been introduced in [7, 5]. In this work, we consider the problem of constructing suitable hydrodynamic approximations for such models.
The present work is devoted to the simulation of a strongly magnetized plasma considered as a mixture of an ion fluid and an electron fluid. For the sake of simplicity, we assume that the model is isothermal and described by Euler equations coupled with a term representing the Lorentz force. Moreover we assume that both Euler systems are coupled through a… (More)
The aim of this article is to construct a BGK-type model for poly-atomic gases which gives in the hydrodynamic limit the proper transport coefficient. Its construction relies upon a systematic procedure: minimizing Boltzmann entropy under suitable moments constraints ([20, 9]). The obtained model corresponds to the ellipsoidal statistical model introduced… (More)
The stationary Boltzmann equation for hard and soft forces in the context of a two component gas is considered in the slab when the molecular masses of the 2 component are different. An L 1 existence theorem is proved when one component satisfies a given indata profile and the other component satisfies diffuse reflection at the boundaries. Weak L 1… (More)
The aim of this paper is to compute viscous correction terms for the isothermal quantum Euler system of Degond, Gallego, Méhats (SIAM Multiscale Model Simul., 6, 2007). We derive this model by using a Chapman-Enskog expansion up to order 1. In a last part, we consider a situation where the flow is nearly irrotational in order to get a simplified model.