8 papers
On "discrete" solutions of the Euler system of gas dynamics
Anna Abbatiello, Eduard Feireisl
The method of Convex Integration has revealed a number of rather disturbing facts concerning well-posedness of the Euler system of gas dynamics. In particular, there is a dense set…
On the stability of solutions to non-Newtonian Navier--Stokes--Fourier-like systems in the supercritical case
Anna Abbatiello, Miroslav Bulíček, Petr Kaplický
We consider a three-dimensional domain occupied by a homogeneous, incompressible, non-Newtonian, heat-conducting fluid with prescribed nonuniform temperature on the boundary and no…
Blow-up criterion for the compressible Navier--Stokes system with inflow-outflow boundary conditions
Anna Abbatiello, Mostafa Meliani
We consider the compressible Navier-Stokes system in three dimensions with general inflow-outflow boundary conditions, meaning that we prescribe a boundary velocity which has non-z…
Generalized dissipative solutions to free boundary compressible viscous models
Anna Abbatiello, Donatella Donatelli
We study free boundary compressible viscous models that may include nonlinear viscosities. These are compressible/incompressible Navier-Stokes type systems for a non-Newtonian stre…
Local existence and conditional regularity for the Navier-Stokes-Fourier system driven by inhomogeneous boundary conditions
Anna Abbatiello, Danica Basaric, Nilasis Chaudhuri +1
We consider the Navier-Stokes-Fourier system with general inhomogeneous Dirichlet-Neumann boundary conditions. We propose a new approach to the local well-posedness problem based o…
On the nonlinear thin obstacle problem
Anna Abbatiello, Giovanna Andreucci, Emanuele Spadaro
The thin obstacle problem or -dimensional Signorini problem is a classical variational problem arising in several applications, starting with its first introduction in elasticit…
On the existence of solutions to generalized Navier--Stokes--Fourier system with dissipative heating
Anna Abbatiello, Miroslav Bulicek, Daniel Lear
We consider a flow of non-Newtonian incompressible heat conducting fluids with dissipative heating. Such system can be obtained by scaling the classical Navier--Stokes--Fourier pro…
On a blow-up criterion for the Navier-Stokes-Fourier system under general equations of state
Anna Abbatiello, Danica Basarić, Nilasis Chaudhuri
In this paper we prove a blow-up criterion for the compressible Navier-Stokes-Fourier system for general thermal and caloric equations of state with inhomogeneous boundary conditio…