Scaling limits for SPDEs with transport noise

Galeati Lucio, EPFL

In this talk, I will present an overview about the progresses that have been made in the last five years on a specific scaling limit, concerning a sequence of Stratonovich transport noises which become concentrated on higher and higher Fourier modes. Solutions to suitable linear and nonlinear SPDE subject to such noise are expected to converge in the limit to solutions of the analogous deterministic PDE where the noise is replaced by a multiple of the Laplacian, which can be interpreted as the emergence of an eddy viscosity. This scaling limit has been rigorously established for many PDEs and has interesting consequence, like: i) estimates for mixing and enhanced dissipation effects for transport equations; ii) regularization by noise and suppression of blow-up for parabolic SPDEs, most notably 3D Navier-Stokes; iii) convergence of hyperbolic-type SPDEs to deterministic parabolic ones, like the stochastic 2D Euler to the deterministic 2D Navier-Stokes. Based on joint works with F. Flandoli and D. Luo.

Area: IS11 - Stochastic Fluid Dynamics (Francesco Grotto)

Keywords: Transport noise; Scaling limit; Stochastic Navier-Stokes.

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