Fractional diffusion limit for collisional kinetic equations: A moments method

Details Fractional diffusion limit for collisional kinetic equations: A moments method Fractional diffusion limit for collisional kinetic equations: A moments method

2009-10-08

arxiv.org/abs/0910.1570v1

Mathematics

Analysis of PDEs

Scientific paper

This paper is devoted to hydrodynamic limits of linear kinetic equations when the thermodynamical equilibrium is described by a heavy-tail distribution function rather than a Maxwellian distribution. We show that the long time/small mean free path behavior of the solution of the kinetic equation is described by a fractional diffusion equation. The method that we introduce is somewhat reminiscent of the so-called "moments method" which plays an important role in kinetic theory.

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