Diffusive Limit of a Kinetic Model for Cometary Flows |
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Authors: | Jan Haskovec and Christian Schmeiser |
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Affiliation: | (1) Institute for Analysis and Scientific Computing, Vienna University of Technology, Vienna, Austria;(2) Faculty of Mathematics, University of Vienna, Vienna, Austria;(3) RICAM, Linz, Austria |
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Abstract: | A kinetic equation with a relaxation time model for wave-particle collisions is considered. Similarly to the BGK-model of gas dynamics, it involves a projection onto the set of equilibrium distributions, nonlinearly dependent on the moments of the distribution function. Under a diffusive and low Mach number scaling the macroscopic limit is a generalization of the incompressible Navier-Stokes equations, where the momentum equations are coupled to a diffusive equation for an energy distribution function. By a moment approximation, this system can be related to a low Mach number model of fluid mechanics, which already appeared in the literature. Finally, for a linearized version corresponding to Stokes flow an existence result for initial value problems is proved. |
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Keywords: | Kinetic equation Wave-particle collision operator Cometary flows Diffusive scaling Macroscopic limit Low Mach number model |
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