Scaling limits of SPDEs with transport noise


This talk is based on a series of works made in collaboration with F. Flandoli and D. Luo in which we explore the effect of transport-type noise to (linear and nonlinear) PDEs. As a paradigmatic example I will focus mostly on stochastic 2D Euler in vorticity form; the structure of the noise comes from the Kraichnan model of turbulence and aims at modelling the small scale behaviour of the solution itself. In a suitable scaling limit of the noise, any solution to the stochastic 2D Euler equation converges to the one of the deterministic 2D Navier-Stokes; this inverts the classical paradigm where solutions to Euler are obtained by a vanishing viscosity limit of Navier-Stokes. The techniques we recently developed ( the aforementioned convergence, when measured in suitable mixing norms.

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