The concept of the slow invariant manifold is recognized as the central idea underpinning a
transition from micro to macro and model reduction in kinetic theories. We present the …

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 …

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We prove nonlinear asymptotic stability of a large class of monotonic shear flows among
solutions of the 2D Euler equations in the channel $\mathbb {T}\times [0, 1] $. More …

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 …

We give a new, simpler, but also and most importantly more general and robust, proof of
nonlinear Landau damping on T^ d T d in Gevrey-1 s-1 s regularity (s> 1/3 s> 1/3) which …

We prove asymptotic stability of the Couette flow for the 2D Euler equations in the domain T
* 0, 1 T× 0, 1. More precisely we prove that if we start with a small and smooth perturbation …

It has been thought for a while that the Prandtl system is only well-posed under the Oleinik
monotonicity assumption or under an analyticity assumption. We show that the Prandtl …

We give an overview of the ideas central to some recent developments in the ergodic theory
of the stochastically forced Navier Stokes equations and other dissipative stochastic partial …