We prove asymptotic stability of shear flows close to the planar Couette flow in the 2D
inviscid Euler equations on T× R. That is, given an initial perturbation of the Couette flow …

We develop a framework for dimension reduction, mode decomposition, and nonparametric
forecasting of data generated by ergodic dynamical systems. This framework is based on a …

The paper is concerned with the problem of regularization by noise of 3D Navier–Stokes
equations. As opposed to several attempts made with additive noise which remained …

The fully parabolic Keller--Segel system is coupled to the incompressible Navier--Stokes
equations through transport and buoyancy. It is shown that when posed with no-flux/no …

In this work we study the long time inviscid limit of the two dimensional Navier–Stokes
equations near the periodic Couette flow. In particular, we confirm at the nonlinear level the …

We study Sobolev regularity disturbances to the periodic, plane Couette flow in the 3D
incompressible Navier-Stokes equations at high Reynolds number Re. Our goal is to …

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 …

Euler equations of incompressible fluids use and enrich many branches of mathematics,
from integrable systems to geometric analysis. They present important open physical and …

For some deterministic nonlinear PDEs on the torus whose solutions may blow up in finite
time, we show that, under suitable conditions on the nonlinear term, the blow-up is delayed …

We analyze the decay and instant regularization properties of the evolution semigroups
generated by two-dimensional drift-diffusion equations in which the scalar is advected by a …