| Abstract: |
| Motivated by fluctuating hydrodynamics, modelling of turbulent fluids, and previous analysis of the Landau-Lifschitz-Navier-Stokes equations, we study a dynamical large deviation principle for solutions to a Galerkin approximation of the stochastic 3D Euler equations; here the noise is divergence free, of Stratonovich transport type, and we consider a scaling regime where the noise intensity $\varepsilon$ and the inverse of the Fourier truncation parameter $N$ go to zero simultaneously. We first show the validity of both a restricted lower bound and an upper bound on compact sets, for a natural choice of rate function, concerning $L^2$-valued admissible weak solutions of the associated skeleton Euler equations. Exploiting the dynamical reversibility of the system, we then show the existence of energy inadmissible solutions, which must be seen by any extension of the rate function which results into a global LDP lower bound. Finally, we extend the LDP upper bound to a global one, by considering a newly introduced concept of H-measure-valued solutions to skeleton Euler.
Based on joint work with Daniel Heydecker (Oslo). |
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