Publications by Michele Dolce | EPFL Graph Search

Self‐similar instability and forced nonuniqueness: An application to the 2D euler equations

Building on an approach introduced by Golovkin in the ’60s, we show that nonuniqueness in some forced partial differential equations is a direct consequence of the existence of a self‐similar linearly unstable eigenvalue: the key point is a clever choice o ...

Wiley2025

Dissipation enhancing properties for a class of Hamiltonian flows with closed streamlines

Massimo Sorella, Carl Johan Peter Johansson, Michele Dolce

We study the evolution of a passive scalar subject to molecular diffusion and advected by an incompressible velocity field on a 2D bounded domain. The velocity field is u=del perpendicular to H, where H is an autonomous Hamiltonian whose level sets are Jor ...

TAYLOR & FRANCIS INC2025

Taylor dispersion and phase mixing in the non-cutoff Boltzmann equation on the whole space

Michele Dolce

In this paper we describe the long-time behavior of the non-cutoff Boltzmann equation with soft potentials near a global Maxwellian background on the whole space in the weakly collisional limit (that is, infinite Knudsen number (Formula presented.)). Speci ...

2024

On the convergence rates of discrete solutions to the Wave Kinetic Equation†

Michele Dolce

In this paper, we consider the long-term behavior of some special solutions to the Wave Kinetic Equation. This equation provides a mesoscopic description of wave systems interacting nonlinearly via the cubic NLS equation. Escobedo and Velázquez showed that ...

2024

Diffusion Enhancement and Taylor Dispersion for Rotationally Symmetric Flows in Discs and Pipes

Michele Dolce

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 three-dimensional infi ...

2024

Stability Threshold of the 2D Couette Flow in a Homogeneous Magnetic Field Using Symmetric Variables

Michele Dolce

We consider a 2D incompressible and electrically conducting fluid in the domain T x R. The aim is to quantify stability properties of the Couette flow (y, 0) with a constant homogenous magnetic field (beta, 0) when |beta|>1/2. The focus lies on the regime ...

Springer2024

Nonlinear inviscid damping and shear-buoyancy instability in the two-dimensional Boussinesq equations

Michele Dolce

We investigate the long-time properties of the two-dimensional inviscid Boussinesq equations near a stably stratified Couette flow, for an initial Gevrey perturbation of size & epsilon;. Under the classical Miles-Howard stability condition on the Richardso ...

WILEY2023