В работе дан обзор исследований последнего десятилетия и приведены новые
результаты по различным новым модификациям классической задачи Канторовича …

VI Bogachev, “Kantorovich problem of optimal transportation of measures: new directions of
research”, Uspekhi Mat. Nauk, 77:5(467) (2022), 3–52; Russian Math. Surveys, 77:5 (2022) …

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 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 …

We put forward a new method for obtaining quantitative lower bounds on the top Lyapunov
exponent of stochastic differential equations. Our method combines (i) a new identity …

This book is dedicated to the qualitative theory of the stochastic one-dimensional Burgers
equation with small viscosity under periodic boundary conditions and to interpreting the …

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 study measurable dependence of measures on a parameter in the following two
classical problems: constructing conditional measures and the Kantorovich optimal …

This paper concerns the forced stochastic Navier-Stokes equation driven by additive noise
in the three dimensional Euclidean space. By constructing an appropriate forcing term, we …