These notes originated from a series of lectures given at Waseda University in April–May
2021, supported by Top Global University Project of Waseda University. The first author …

2D Smagorinsky-Type Large Eddy Models as Limits of Stochastic PDEs | Journal of Nonlinear
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A stochastic version of the two-layer quasi-geostrophic model (2LQG) with multiplicative
transport noise is analysed. This popular intermediate complexity model describes large …

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 …

Diffusion with stochastic transport is investigated here when the random driving process is a
very general Gaussian process including Fractional Brownian motion. The purpose is the …

We consider the stochastic inviscid Leray-α model on the torus driven by transport noise.
Under a suitable scaling of the noise, we prove that the weak solutions converge, in some …

The velocity field, white in time and modelling phenomenologically a turbulent fluid, acts on
the magnetic field as a transport-stretching noise. We prove, in a quantitative way, that, in the …

We consider stochastic inviscid dyadic models with energy-preserving noise. It is shown that
the models admit weak solutions which are unique in law. Under a certain scaling limit of the …

The phenomenon of dissipation enhancement by transport noise is shown for stochastic 2D
Navier–Stokes equations in velocity form. In the 3D case, suppression of blow-up is proved …

The aim of this work is to present, in a compact way, the latest results about the dissipation
properties of transport noise in fluid mechanics. Starting from the reasons why transport …