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| Fractional diffusion limits have been derived for collisional kinetic models conserving only the total mass (0-th moment). Their derivation is due, mainly, to the presence of a heavily tailed equilibrium distribution function in the collisional operator (instead of a Maxwellian) and a particular rescaling in time. In the present work, we extend the previous results to a linear kinetic model conserving the first three moments. Our approach is based on the `moments methods' introduced by Antoine Mellet. In the limit we obtain the Stokes equation with fractional laplacian, under some conditions. This is a joint work with Sabine Hittmeir from Technische Universitat of Vienna. |
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