Related papers: Enhanced dissipation, hypoellipticity, and anomalo…

We consider the dissipative generalized Surface Quasi-Geostrophic equation with dissipation given by any fractional power of the Laplacian. In the inviscid limit, it is proved that anomalous dissipation of the Hamiltonian is prevented by…

In this paper, we studied the long-wave instability of the shear flows. When the wavenumber of perturbation is larger than the critical value, the flow is always neutrally stable. First, we obtain a new upper bound for the neutral…

We seek to quantify non-normality of the most amplified resolvent modes and predict their features based on the characteristics of the base or mean velocity profile. A 2-by-2 model linear Navier-Stokes (LNS) operator illustrates how…

We prove asymptotic stability of shear flows in a neighborhood of the Couette flow for the 2D Euler equations in the domain $\T\times[0,1]$. More precisely we prove that if we start with a small and smooth perturbation (in a suitable Gevrey…

We study the linear asymptotic stability of stably stratified monotone shear flows for the Boussinesq equations in the periodic channel. By means of the limiting absorption principle, we obtain a precise description of the inviscid damping…

The diffusive properties in velocity fields whose small scales are parameterized by non $\delta$-correlated noise is investigated using multiscale technique. The analytical expression of the eddy diffusivity tensor is found for a 2D steady…

Much effort has been spent in recent years on restoring uniqueness of McKean-Vlasov SDEs with non-smooth coefficients. As a typical instance, the velocity field is assumed to be bounded and measurable in its space variable and…

We establish explicit lower bounds for advection-diffusion equations in three settings: a polynomial $\dot H^{-1}$ bound for inviscid shears with $u\in L^\infty_t W^{1,1}_y$, a uniform positive lower bound on the mixing scale for diffusive…

Mixing a passive scalar field by stirring can be measured in a variety of ways including tracer particle dispersion, via the flux-gradient relationship, or by suppression of scalar concentration variations in the presence of inhomogeneous…

In this paper we discuss the dynamical features of intermittent fluctuations in homogeneous shear flow turbulence. In this flow the energy cascade is strongly modified by the production of turbulent kinetic energy related to the presence of…

We study the reflection of an acoustic plane wave from a steadily sliding planar interface with velocity strengthening friction or a shear band in a confined granular medium. The corresponding acoustic impedance is utterly different from…

This is the first part in a series of two papers that concern with the quantitative analysis of the electromagnetic field enhancement and anomalous diffraction by a periodic array of subwavelength slits. The scattering problem in the…

We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on $\mathbb{T} \times \mathbb{R}$ with small viscosity $\nu$. We establish nonlinear stability in $H^s$ for $s \geq 2$ with…

In this note, we study the long-time dynamics of passive scalars driven by rotationally symmetric flows. We focus on identifying precise conditions on the velocity field in order to prove enhanced dissipation and Taylor dispersion in…

We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical…

First, we consider Kolmogorov flow (a shear flow with a sinusoidal velocity profile) for 2D Navier-Stokes equation on a torus. Such flows, also called bar states, have been numerically observed as one type of metastable states in the study…

We study the stationary and transient behaviors of the microemulsion phase subjected to a shear flow. The system is described by a diffusion-convective equation which generalizes the usual Cahn-Hilliard equation. Non-linear terms are…

We obtain several new regularity results for solutions of scalar conservation laws satisfying the genuine nonlinearity condition. We prove that the solutions are continuous outside of the jump set, which is codimension one rectifiable. We…

In this paper, we prove that the $L^2$ norm of spatial mean-free solutions to the advection--diffusion equation on $\mathbb{T}^2$ with shear drifts satisfies an \emph{exponential lower bound} in time. This lower bound shows that diffusion…

We prove decay estimates in the interior for solutions to elliptic equations in divergence form with Lipschitz continuous coefficients. The estimates explicitly depend on the distance from the boundary and on suitable notions of frequency…