52 citations · 207 across the 36 of their papers we have counts for
41 papers
Invariant measures for the one-dimensional stochastic Navier-Stokes-Korteweg equations
Donatella Donatelli, Lorenzo Pescatore, Stefano Spirito
We investigate the long-time behaviour of a one-dimensional compressible viscous fluid with general capillarity and density dependent viscosity, driven by a stochastic additive noi…
Global Existence and Uniqueness of Strong Solutions for a Phase Transition Model in Atmospheric Dynamics
Giada Cianfarani Carnevale, Donatella Donatelli, Stefano Spirito
In this work, we study a phase transition model in atmospheric dynamics, inspired by the works [6,14,15], which analyze the primitive equations governing the evolution of velocity,…
On the existence of non-negative weak solutions for fourth order equations of gradient flow type
Stefanos Georgiadis, Stefano Spirito
In this paper, we consider a family of one-dimensional fourth order evolution equations arising as gradient flows of the Korteweg energy, i.e. the -norm of the first derivativ…
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…
Convergence of the Euler-Voigt equations to the Euler equations in two dimensions
Stefano Abbate, Luigi C. Berselli, Gianluca Crippa +1
In this paper, we consider the two-dimensional torus and we study the convergence of solutions of the Euler-Voigt equations to solutions of the Euler equations, under several regul…
Global weak solutions of the Navier-Stokes-Korteweg Equations in one dimension
Paolo Antonelli, Didier Bresch, Stefano Spirito
We prove the global existence of weak solutions of the one-dimensional Navier-Stokes-Korteweg (NSK) equations when the viscosity and the capillarity coefficients are power function…
Weak martingale solutions to the stochastic 1D Quantum-Navier-Stokes equations
Donatella Donatelli, Lorenzo Pescatore, Stefano Spirito
In this paper we prove the existence of global weak dissipative martingale solutions for a one-dimensional compressible fluid model with capillarity and density dependent viscosity…
Asymptotic Limits for Strain-Gradient Viscoelasticity with Nonconvex Energy
Aseel AlNajjar, Stefano Spirito, Athanasios E. Tzavaras
We consider the system of viscoelasticity with higher-order gradients and nonconvex energy in several space dimensions. We establish the asymptotic limits when the viscosity $ν\rig…
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…
Global regularity for the one-dimensional stochastic Quantum-Navier-Stokes equations
Donatella Donatelli, Lorenzo Pescatore, Stefano Spirito
In this paper we prove the global in time well-posedness of strong solutions to the Quantum-Navier-Stokes equation driven by random initial data and stochastic external force. In p…
Strong convergence of the vorticity and conservation of the energy for the -Euler equations
Stefano Abbate, Gianluca Crippa, Stefano Spirito
In this paper, we study the convergence of solutions of the -Euler equations to solutions of the Euler equations on the -dimensional torus. In particular, given an initial vo…
On the convergence of second-order in time numerical discretizations for the evolution Navier-Stokes equations
Luigi C. Berselli, Stefano Spirito
We prove the convergence of certain second-order numerical methods to weak solutions of the Navier-Stokes equations satisfying in addition the local energy inequality, and therefor…
Existence and uniqueness for a viscoelastic Kelvin-Voigt model with nonconvex stored energy
Konstantinos Koumatos, Corrado Lattanzio, Stefano Spirito +1
We consider nonlinear viscoelastic materials of Kelvin-Voigt type with stored energies satisfying an Andrews-Ball condition, allowing for non convexity in a compact set. Existence…
Relaxation limit from the Quantum-Navier-Stokes equations to the Quantum Drift Diffusion equation
Paolo Antonelli, Giada Cianfarani Carnevale, Corrado Lattanzio +1
The relaxation-time limit from the Quantum-Navier-Stokes-Poisson system to the quantum drift-diffusion equation is performed in the framework of finite energy weak solutions. No as…
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…
Global existence of finite energy weak solutions to the Quantum Navier-Stokes equations with non-trivial far-field behavior
Paolo Antonelli, Lars Eric Hientzsch, Stefano Spirito
We prove global existence of finite energy weak solutions to the quantum Navier-Stokes equations in the whole space with non trivial far-field condition in dimensions d = 2,3. The…
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…
Global existence of weak solutions to the Navier-Stokes-Korteweg equations
Paolo Antonelli, Stefano Spirito
In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of fin…
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…
Logarithmic estimates for continuity equations
Maria Colombo, Gianluca Crippa, Stefano Spirito
The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [Colombo, Crippa, and Spirito, Calc. Var. Partial…
Strong continuity for the 2D Euler equations
Gianluca Crippa, Elizaveta Semenova, Stefano Spirito
We prove two results of strong continuity with respect to the initial datum for bounded solutions to the Euler equations in vorticity form. The first result provides sequential con…
On the compactness of weak solutions to the Navier-Stokes-Korteweg equations for capillary fluids
Paolo Antonelli, Stefano Spirito
In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove compactness of finite e…
Splash singularities for a general Oldroyd model with finite Weissenberg number
Elena Di Iorio, Pierangelo Marcati, Stefano Spirito
In this paper we study a 2D Oldroyd free-boundary model which describes the evolution of a viscoelastic fluid. We prove existence of splash singularities, namely points where the b…