5 papers
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…
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…
The Oberbeck-Boussinesq system with non-local boundary conditions
Anna Abbatiello, Eduard Feireisl
We consider the Oberbeck--Boussinesq system with non--local boundary conditions arising as a singular limit of the full Navier--Stokes--Fourier system in the regime of low Mach and…