28 citations · 95 across the 21 of their papers we have counts for
21 papers
Magnetic relaxation for the MHD equations via the stable manifold method
Gennaro Ciampa, Renato Lucà
We prove that given any sufficiently small and regular solution of the stationary Euler equations there exists an infinite dimensional family of solutions of the non-re…
On the rate of the vanishing viscosity approximation for Mean Field Games with nonlocal coupling
Gennaro Ciampa, Alessandro Goffi
We study quantitative convergence rates of the vanishing viscosity approximation of first-order time-dependent Mean Field Games with regularizing coupling acting in the Hamilton-Ja…
Large bulk viscosity limit for compressible MHD equations in critical Besov spaces
Gennaro Ciampa, Donatella Donatelli, Giada Pellecchia
We study the large bulk viscosity limit for the compressible magnetohydrodynamics (MHD) equations in two and three dimensions. For arbitrarily large initial data in critical Besov…
Accelerated and fast magnetic reconnection through enhanced resistive dissipation for MHD equations
Gennaro Ciampa, Renato Lucà
We consider the phenomenon of magnetic reconnection, namely a change in the topology of magnetic lines, for sufficiently regular solutions of the three-dimensional periodic magneto…
A priori error estimates for the -method for the flow of nonsmooth velocity fields
Gennaro Ciampa, Tommaso Cortopassi, Gianluca Crippa +2
Velocity fields with low regularity (below the Lipschitz threshold) naturally arise in many models from mathematical physics, such as the inhomogeneous incompressible Navier-Stokes…
Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations
Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
The aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of log…
Large amplitude traveling waves for the non-resistive MHD system
Gennaro Ciampa, Riccardo Montalto, Shulamit Terracina
We prove the existence of large amplitude bi-periodic traveling waves (stationary in a moving frame) of the two-dimensional non-resistive Magnetohydrodynamics (MHD) system with a t…
Localization of Beltrami fields: global smooth solutions and vortex reconnection for the Navier-Stokes equations
Gennaro Ciampa, Renato Lucà
We introduce a class of divergence-free vector fields on obtained after a suitable localization of Beltrami fields. First, we use them as initial data to construct u…
A regularity result for the Fokker-Planck equation with non-smooth drift and diffusion
Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
The goal of this paper is to study weak solutions of the Fokker-Planck equation. We first discuss existence and uniqueness of weak solutions in an irregular context, providing a un…
Weak and parabolic solutions of advection-diffusion equations with rough velocity field
Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
We study the Cauchy problem for the advection-diffusion equation associated with a merely integrable divergence-free vector field defi…
Viscoelasticity, logarithmic stresses, and tensorial transport equations
Gennaro Ciampa, Giulio G. Giusteri, Alessio G. Soggiu
We introduce models for viscoelastic materials, both solids and fluids, based on logarithmic stresses to capture the elastic contribution to the material response. The matrix logar…
On the topology of the magnetic lines of solutions of the MHD equations
Gennaro Ciampa
We construct examples of smooth periodic solutions to the Magnetohydrodynamic equations in dimension 2 with positive resistivity for which the topology of the magnetic lines change…
Magnetic Reconnection in Magnetohydrodynamics
Pedro Caro, Gennaro Ciampa, Renato Lucà
We provide examples of periodic solutions (in both 2 and 3 dimension) of the Magnetohydrodynamics equations such that the topology of the magnetic lines changes during the evolutio…
Vanishing viscosity in mean-field optimal control
Gennaro Ciampa, Francesco Rossi
We show the existence of Lipschitz-in-space optimal controls for a class of mean-field control problems with dynamics given by a non-local continuity equation. The proof relies on…
On the advection-diffusion equation with rough coefficients: weak solutions and vanishing viscosity
Paolo Bonicatto, Gennaro Ciampa, Gianluca Crippa
We deal with the vanishing viscosity scheme for the transport/continuity equation drifted by a divergence-free vector field $\bol…
Vanishing viscosity for linear-quadratic mean-field control problems
Gennaro Ciampa, Francesco Rossi
We consider a mean-field control problem with linear dynamics and quadratic control. We apply the vanishing viscosity method: we add a (regularizing) heat diffusion with a small vi…
Energy conservation for 2D Euler with vorticity in
Gennaro Ciampa
In these notes we discuss the conservation of the energy for weak solutions of the two-dimensional incompressible Euler equations. Weak solutions with vorticity in $L^\infty_t L^p_…
Strong convergence of the vorticity for the 2D Euler Equations in the inviscid limit
Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
In this paper we prove the uniform-in-time convergence in the inviscid limit of a family of solutions of the Navier-Stokes equations towards a renormalized/Lagrang…
Weak solutions obtained by the vortex method for the 2D Euler equations are Lagrangian and conserve the energy
Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
We discuss the Lagrangian property and the conservation of the kinetic energy for solutions of the 2D incompressible Euler equations. Existence of Lagrangian solutions is known whe…
On smooth approximations of rough vector fields and the selection of flows
Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
In this work we deal with the selection problem of flows of an irregular vector field. We first summarize an example from \cite{CCS} of a vector field and a smooth approximatio…
Smooth approximation is not a selection principle for the transport equation with rough vector field
Gennaro Ciampa, Gianluca Crippa, Stefano Spirito
In this paper we analyse the selection problem for weak solutions of the transport equation with rough vector field. We answer in the negative the question whether solutions of the…