In this paper, we consider the forced incompressible Navier–Stokes equations with
vanishing viscosity on the three-dimensional torus. We show that there are (classical) …

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Abstract For every α< 1 3, we construct an explicit divergence-free vector field b (t, x) which
is periodic in space and time and belongs to C t 0 C x α∩ C t α C x 0 such that the …

We study diffusion and mixing in different linear fluid dynamics models, mainly related to
incompressible flows. In this setting, mixing is a purely advective effect that causes a transfer …

Abstract The Obukhov–Corrsin theory of scalar turbulence [,] advances quantitative
predictions on passive-scalar advection in a turbulent regime and can be regarded as the …

We consider the linear transport equations driven by an incompressible flow in dimensions d
≥ 3 d≥ 3. For divergence-free vector fields u ∈ L^ 1_t W^ 1, qu∈ L t 1 W 1, q, the …

We study the mixing and dissipation properties of the advection–diffusion equation with
diffusivity 0< κ ≪ 1 0< κ≪ 1 and advection by a class of random velocity fields on T^ d T d …

In 1959 Batchelor predicted that the stationary statistics of passive scalars advected in fluids
with small diffusivity k should display a power spectrum along an inertial range contained in …

We consider the question of exponential mixing for random dynamical systems on arbitrary
compact manifolds without boundary. We put forward a robust, dynamics-based framework …

We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions of
the stochastically-forced 2D Navier–Stokes equations and 3D hyper-viscous Navier–Stokes …