3,647 research outputs found
Asymptotic behavior of global entropy solutions for nonstrictly hyperbolic systems with linear damping
In this paper we investigate the large time behavior of the global weak
entropy solutions to the symmetric Keyftiz-Kranzer system with linear damping.
It is proved that as t tends to infinite the entropy solutions tend to zero in
the L p nor
Expansion of a compressible gas in vacuum
Tai-Ping Liu \cite{Liu\_JJ} introduced the notion of "physical solution' of
the isentropic Euler system when the gas is surrounded by vacuum. This notion
can be interpreted by saying that the front is driven by a force resulting from
a H\"older singularity of the sound speed. We address the question of when this
acceleration appears or when the front just move at constant velocity. We know
from \cite{Gra,SerAIF} that smooth isentropic flows with a non-accelerated
front exist globally in time, for suitable initial data. In even space
dimension, these solutions may persist for all ; we say that they are
{\em eternal}. We derive a sufficient condition in terms of the initial data,
under which the boundary singularity must appear. As a consequence, we show
that, in contrast to the even-dimensional case, eternal flows with a
non-accelerated front don't exist in odd space dimension. In one space
dimension, we give a refined definition of physical solutions. We show that for
a shock-free flow, their asymptotics as both ends are
intimately related to each other
Embedding initial data for black hole collisions
We discuss isometric embedding diagrams for the visualization of initial data
for the problem of the head-on collision of two black holes. The problem of
constructing the embedding diagrams is explicitly presented for the best
studied initial data, the Misner geometry. We present a partial solution of the
embedding diagrams and discuss issues related to completing the solution.Comment: (27pp text, 11 figures
Global existence of solutions for a multi-phase flow: a drop in a gas-tube
In this paper we study the flow of an inviscid fluid composed by three
different phases. The model is a simple hyperbolic system of three conservation
laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our
main result concerns the global existence of weak entropic solutions to the
initial-value problem for large initial data
Global existence of solutions for a multi-phase flow: a bubble in a liquid tube and related cases
In this paper we study the problem of the global existence (in time) of weak,
entropic solutions to a system of three hyperbolic conservation laws, in one
space dimension, for large initial data. The system models the dynamics of
phase transitions in an isothermal fluid; in Lagrangian coordinates, the phase
interfaces are represented as stationary contact discontinuities. We focus on
the persistence of solutions consisting in three bulk phases separated by two
interfaces. Under some stability conditions on the phase configuration and by a
suitable front tracking algorithm we show that, if the BV-norm of the initial
data is less than an explicit (large) threshold, then the Cauchy problem has
global solutions
Numerical evaluation of heat transfer enhancement due to annular electroconvection induced by injection in a dielectric liquid
Two-dimensional numerical simulations are carried out to evaluate the enhancement of
natural convection heat transfer in a dielectric liquid resulting from injection induced
annular electro-convection. The liquid is confined between two concentric horizontal
cylinders and subjected to the simultaneous actions of a direct current electric field and
a thermal gradient. A unipolar injection from the inner cylinder introduces free space
charges into the liquid. Numerical results are presented for the configuration of inner
to outer diameter ratio of 0.5 and silicon oil as the working medium. It is found that the
charge injection may induce a strong radial fluid motion, which consequently augments
the heat transfer rate. Due to the linear stability nature of electro-convection, there
exists a threshold value of the electric driving parameter, above which the electrical
enhancement becomes manifest. In addition, when the electric driving parameter is
sufficiently high, the flow is fully dominated by the Coulomb force, and thus heat
transfer becomes independent of the thermal driving parameter.Ministerio de Ciencia y Tecnología FIS2011-25161Junta de Andalucía P10-FQM-5735Junta de Andalucía P09-FQM-458
Pointwise Green's function bounds and stability of relaxation shocks
We establish sharp pointwise Green's function bounds and consequent
linearized and nonlinear stability for smooth traveling front solutions, or
relaxation shocks, of general hyperbolic relaxation systems of dissipative
type, under the necessary assumptions ([G,Z.1,Z.4]) of spectral stability,
i.e., stable point spectrum of the linearized operator about the wave, and
hyperbolic stability of the corresponding ideal shock of the associated
equilibrium system. This yields, in particular, nonlinear stability of weak
relaxation shocks of the discrete kinetic Jin--Xin and Broadwell models. The
techniques of this paper should have further application in the closely related
case of traveling waves of systems with partial viscosity, for example in
compressible gas dynamics or MHD.Comment: 120 pages. Changes since original submission. Corrected typos, esp.
energy estimates of Section 7, corrected bad forward references, expanded
Remark 1.17, end of introductio
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