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 …

In this work we consider the Lagrangian properties of a random version of the Arnold-
Beltrami-Childress (ABC) in a three-dimensional periodic box. We prove that the associated …

Mixing in fluid flows is a ubiquitous phenomenon and arises in many situations ranging from
everyday occurrences, such as mixing of cream in coffee, to fundamental physical …

We show exponential mixing of passive scalars advected by a solution to the stochastic
Navier-Stokes equations with finitely many (eg four) forced modes satisfying a hypoellipticity …

We consider the three-dimensional parabolic-parabolic Patlak-Keller-Segel equations (PKS)
subject to ambient flows. Without the ambient fluid flow, the equation is super-critical in three …

We study the passive transport of a scalar field by a spatially smooth but white-in-time
incompressible Gaussian random velocity field on\(\mathbb {R}^ d\). If the velocity field u is …

We consider the three-dimensional parabolic-parabolic Patlak-Keller-Segel equations (PKS)
subject to ambient flows. Without the ambient fluid flow, the equation is super-critical in three …

We study the passive transport of a scalar field by a spatially smooth but white-in-time
incompressible Gaussian random velocity field on $\mathbb {R}^ d $. If the velocity field $ u …

We consider a fluid governed by the randomly forced 2D Navier-Stokes system. It is
assumed that the force is bounded, acts directly only on a small number of Fourier modes …

The main goal of this work is to provide a description of transitions from uniform to non-
uniform snychronization in diffusions based on large deviation estimates for finite time …