In this paper, we prove the linear inviscid dam** and vorticity depletion phenomena for the
linearized Euler equations around the Kolmogorov flow. These results confirm Bouchet and …

Kramers' law describes the mean transition time of an overdamped Brownian particle
between local minima in a potential landscape. We review different approaches that have …

Quasi-stationary, or metastable, states play an important role in two-dimensional turbulent
fluid flows, where they often emerge on timescales much shorter than the viscous timescale …

The purpose of this article is to introduce a diffusion model for biological organisms that
increase their motility when food or other resource is insufficient. It is shown in this paper that …

In this work, we consider the forced generalized Burgers-Huxley equation and establish the
existence and uniqueness of a global weak solution using a Faedo-Galerkin approximation …

We present a class of efficient parametric closure models for 1D stochastic Burgers
equations. Casting it as statistical learning of the flow map, we derive the parametric form by …

In this paper, we study the linear metastability for the linearized 2D dissipative surface quasi-
geostrophic equation with small viscosity ν around the quasi-steady state Θ sin=-e-ν t sin y …

Plant autotoxicity has proved to play an essential role in the behaviour of local vegetation.
We analyse a reaction–diffusion-ODE model describing the interactions between vegetation …

In this paper we propose the first framework to study Burgers' equation featuring critical fast
diffusion in form of $ u_t+ f (u) _x=(\ln u) _ {xx} $. The solution possesses a strong singularity …

The study of fluid motions is of obvious importance for a host of applications ranging in scale
from the microscopic to the atmospheric. Since we live in a three-dimensional world, it may …