LDP and CLT for SPDEs with Transport Noise

Understand

In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term.

• Large deviations and Gaussian fluctuations underlying such scaling limit are investigated in two cases of interest: stochastic linear transport equations in dimension $D\geq 2$ and $2$D Euler equations in vorticity form.
• In both cases, a central limit theorem with strong convergence and explicit rate is established.
• The proofs rely on nontrivial tools, like the solvability of transport equations with supercritical coefficients and $\Gamma$-convergence arguments.