863 research outputs found
Weak solutions to the barotropic Navier-Stokes system with slip boundary conditions in time dependent domains
We consider the compressible (barotropic) Navier-Stokes system on
time-dependent domains, supplemented with slip boundary conditions. Our
approach is based on penalization of the boundary behaviour, viscosity, and the
pressure in the weak formulation. Global-in-time weak solutions are obtained
Scale interactions in compressible rotating fluids
We study a triple singular limit for the scaled barotropic Navier-Stokes
system modeling the motion of a rotating, compressible, and viscous fluid,
where the Mach and Rossby numbers are proportional to a small parameter, while
the Reynolds number becomes infinite. If the fluid is confined to an infinite
slab bounded above and below by two parallel planes, the limit behavior is
identified as a purely horizontal motion of an incompressible inviscid fluid,
the evolution of which is described by an analogue of the Euler system
On a non-isothermal model for nematic liquid crystals
A model describing the evolution of a liquid crystal substance in the nematic
phase is investigated in terms of three basic state variables: the {\it
absolute temperature} \teta, the {\it velocity field} \ub, and the {\it
director field} \bd, representing preferred orientation of molecules in a
neighborhood of any point of a reference domain. The time evolution of the
velocity field is governed by the incompressible Navier-Stokes system, with a
non-isotropic stress tensor depending on the gradients of the velocity and of
the director field \bd, where the transport (viscosity) coefficients vary
with temperature. The dynamics of \bd is described by means of a parabolic
equation of Ginzburg-Landau type, with a suitable penalization term to relax
the constraint |\bd | = 1. The system is supplemented by a heat equation,
where the heat flux is given by a variant of Fourier's law, depending also on
the director field \bd. The proposed model is shown compatible with
\emph{First and Second laws} of thermodynamics, and the existence of
global-in-time weak solutions for the resulting PDE system is established,
without any essential restriction on the size of the data
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