Description
After discussing the problematic of hydrodynamical limits in
the context of gas dynamics for the Boltzmann equation, we took an
interest in the more general context of BGK models which are some
kinetic equations. More precisely, we study a stochastic BGK model with
a high field scaling as an approximation of a hyperbolic conservation
law with stochastic forcing. After establishing the existence of a
solution for any fixed parameter $\varepsilon$, we prove the convergence
to a kinetic equation where a modified Maxwellian appears under an
additional assumption on these solutions. We deduce from it the
existence of a weak solution to the studied scalar conservation law with
stochastic forcing.