On Large Deviation Principle and inviscid hydrodynamical models
Résumé
We present some recent results jointly proven with H. Bessaih about a Large Deviations Principle for solutions to stochastic hydrodynamical equations when the viscosity coefficient converges to 0 and the multiplicative noise is multiplied by its square root. The good rate function is described in terms of the solution to a deterministic inviscid control equation, which is more irregular in the space variable than the solution to the SPDE. This forces us to use either a smaller space or a weaker topology than the "natural ones". The proof uses the weak convergence approach to LDP.