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arXiv · 2510.16894

On a repulsion model with Coulomb interaction and nonlinear mobility

Antonin Chodron de Courcel·Charles Elbar
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Abstract

We study a scalar conservation law on the torus in which the flux $\mathbf{j}$ is composed of a Coulomb interaction and a nonlinear mobility: $\mathbf{j} = -u^m\nabla\mathsf{g}\ast u$. We prove existence of entropy solutions and a weak-strong uniqueness principle. We also prove several properties shared among entropy solutions, in particular a lower barrier in the fast diffusion regime $m\lt 1$. In the porous media regime $m\ge 1$, we study the decreasing rearrangement of solutions, which allows to prove an instantaneous growth of the support and a waiting time phenomenon. We also show exponential convergence of the solutions towards the spatial average in several topologies.

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Antonin Chodron de Courcel, Charles Elbar. 2025-10-19. On a repulsion model with Coulomb interaction and nonlinear mobility. https://arxiv.org/abs/2510.16894

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