Invariant measures for stochastic conservation laws
- Arnaud Debussche (Ecole normale supérieure de Rennes, France)
We study periodic scalar first-order conservation laws with stochastic forcing. Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour in any space dimension. For sub-cubic fluxes, we show the existence of an invariant measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the invariant measure.