Fethi Ben Belgacem

F. Ben Belgacem, P-E Jabin

We prove quantitative regularity estimates for the solutions to non-linear continuity equations and their discretized numerical approximations on Cartesian grids when advected by a rough force field. This allow us to recover the known optimal regularity for linear transport equations but also to obtain the convergence of a wide range of numerical schemes. Our proof is based on a novel commutator estimates, quantifying and extending to the non-linear case the classical commutator approach of the theory of renormalized solutions.

Fethi Ben Belgacem

In this paper we investigate the hydrodynamic limit of the Boltzmann-Monge-Ampere system in the so-called quasineutral regime. We prove the convergence of the Boltzmann-Monge-Ampere system to the Euler equation by using the relative entropy method.