Fractional-diffusion-advection limit of a kinetic model (Q2817444)

This paper is concerned with the study of a fractional diffusion equation with advection term. This problem is motivated by a kinetic transport model with a linear turning operator, which is in relationship with the fat-tailed equilibrium distribution and a small directional bias due to a given vector field. The analysis developed in this paper strongly relies on bounds derived by relative entropy inequalities and on two recently developed approaches for the macroscopic limit. These are: (i) a Fourier-Laplace transform method for spatially homogeneous data and (ii) the moment method, which is based on a modified test function. The derivation of several uniform (in the small parameter \(\varepsilon\)) bounds on the solution is developed in the final section of this paper.