arXiv subjects

Stefano Spirito

Publications and source records attributed to Stefano Spirito.

40 records · Page 3Linked to original sources

arXiv2014

Renormalized solutions to the continuity equation with an integrable damping term

We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions proved that, when the damping term is bounded in space and time, the equation is well posed in the class of distributional solutions and the solution is transported by suitable characteristics of the vector field. In this paper, we prove existence and uniqueness of renormalized solutions in the case of an integrable damping term, employing a new logarithmic estimate inspired by analogous ideas of Ambrosio, Lecumberry, and Maniglia, Crippa and De Lellis in the Lagrangian case.

math.AP↗

arXiv2014

Renormalized solutions of the 2d Euler equations

In this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized.

math.AP↗

arXiv2012

Inviscid limits for the 3D Navier-Stokes equations with slip boundary conditions and applications to the 3D Boussinesq equations

In this note we consider the inviscid limit for the 3D Boussinesq equations without diffusion, under slip boundary conditions of Navier's type. We first study more closely the Navier-Stokes equations, to better understand the problem. The role of the initial data is also emphasized in connection with the vanishing viscosity limit.

math.AP↗

arXiv2011

Convergence of Ginzburg-Landau Approximations for a Liquid Crystal Flow in 2D

In this paper we prove the convergence for all time for a Ginzburg- Landau type approximation of a simplified Ericksen-Leslie model in two dimension. Moreover, we are able to show that the singular set consists in at most finitely many singular points and we give a characterizations of the singularities.

math.AP↗