332 research outputs found
On a class of generalized solutions to equations describing incompressible viscous fluids
We consider a class of viscous fluids with a general monotone dependence of
the viscous stress on the symmetric velocity gradient. We introduce the concept
of dissipative solution to the associated initial boundary value problem
inspired by the measure-valued solutions for the inviscid (Euler) system. We
show the existence as well as the weak-strong uniqueness property in the class
of dissipative solutions. Finally, the dissipative solution enjoying certain
extra regularity coincides with a strong solution of the same problem
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
A rigorous derivation of the stationary compressible Reynolds equation via the Navier-Stokes equations
We provide a rigorous derivation of the compressible Reynolds system as a
singular limit of the compressible (barotropic) Navier-Stokes system on a thin
domain. In particular, the existence of solutions to the Navier-Stokes system
with non-homogeneous boundary conditions is shown that may be of independent
interest. Our approach is based on new a priori bounds available for the
pressure law of hard sphere type. Finally, uniqueness for the limit problem is
established in the 1D case
Inviscid incompressible limits of the full Navier-Stokes-Fourier system
We consider the full Navier-Stokes-Fourier system in the singular limit for
the small Mach and large Reynolds and Peclet numbers, with ill prepared initial
data on the three dimensional Euclidean space. The Euler-Boussinesq
approximation is identified as the limit system
Multi-scale analysis of compressible viscous and rotating fluids
We study a singular limit for the compressible Navier-Stokes system when the
Mach and Rossby numbers are proportional to certain powers of a small parameter
\ep. If the Rossby number dominates the Mach number, the limit problem is
represented by the 2-D incompressible Navier-Stokes system describing the
horizontal motion of vertical averages of the velocity field. If they are of
the same order then the limit problem turns out to be a linear, 2-D equation
with a unique radially symmetric solution. The effect of the centrifugal force
is taken into account
Sensitivity analysis of 1-d steady forced scalar conservation laws
We analyze 1 - d forced steady state scalar conservation laws. We first show the existence and uniqueness of entropy solutions as limits as t→ ∞ of the corresponding solutions of the scalar evolutionary hyperbolic conservation law. We then linearize the steady state equation with respect to perturbations of the forcing term. This leads to a linear first order differential equation with, possibly, discontinuous coefficients. We show the existence and uniqueness of solutions in the context of duality solutions. We also show that this system corresponds to the steady state version of the linearized evolutionary hyperbolic conservation law. This analysis leads us to the study of the sensitivity of the shock location with respect to variations of the forcing term, an issue that is relevant in applications to optimal control and parameter identification problems
Ill-posedness for the full euler system driven by multiplicative white noise
We consider the Euler system describing the motion of a compressible fluid driven by a multiplicative white noise. We identify a large class of initial data for which the problem is ill posed-there exist infinitely many global in time weak solutions. The solutions are adapted to the noise and satisfy the entropy admissibility criterion
Small business incubators: An emerging phenomenon in South Africa’s SMME economy
In South Africa much policy attention is focused on the potential of the small, medium and micro-enterprise
(SMME) economy for job creation. Nevertheless, despite government support for the SMME economy, high
mortality rates are experienced by start-up enterprises. In common with international experience South Africa
has adopted business incubation as a strategic tool for assisting the survival as well as building the
competitiveness of SMMEs. This article analyses the state of business incubation in South Africa drawing
attention to marked differences between the groups of public sector business incubators as opposed to those
business incubators which have been initiated by the private sector
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