Abstract:
We propose a mathematical model describing the transport of sand grains driven by wind, coupled with the evolution of the air momentum, within a bounded domain of $\mathbb{R}^2$. The sand grains are assumed to be spherical, of constant mass, and are modeled at a mesoscopic scale by a particle density function, while the wind is described at a macroscopic scale by a mean velocity field. We focus on the stationary regime of the system, corresponding to an equilibrium state under constant conditions. The analysis consists of solving the transport equation along characteristics for a given velocity field, followed by the study of the stationary wind equation using Schauder's fixed-point theorem.
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