86,595 research outputs found
Incompressible Limit of Solutions of Multidimensional Steady Compressible Euler Equations
A compactness framework is formulated for the incompressible limit of
approximate solutions with weak uniform bounds with respect to the adiabatic
exponent for the steady Euler equations for compressible fluids in any
dimension. One of our main observations is that the compactness can be achieved
by using only natural weak estimates for the mass conservation and the
vorticity. Another observation is that the incompressibility of the limit for
the homentropic Euler flow is directly from the continuity equation, while the
incompresibility of the limit for the full Euler flow is from a combination of
all the Euler equations. As direct applications of the compactness framework,
we establish two incompressible limit theorems for multidimensional steady
Euler flows through infinitely long nozzles, which lead to two new existence
theorems for the corresponding problems for multidimensional steady
incompressible Euler equations.Comment: 17 pages; 2 figures. arXiv admin note: text overlap with
arXiv:1311.398
Galerkin Least-Squares Stabilization Operators for the Navier-Stokes Equations : A Unified Approach
In this dissertation we attempt to approach fluid mechanics problems from a unified point of view and to combine techniques developed originally for compressible or incompressible flows into a more general framework. In order to study the viability of a unified approach, it is necessary to choose a starting formulation, therefore the choice of variables in the governing equations is crucial. For example, conservative variables are not suitable for a unified formulation because they result in a singular limit for incompressible flows. When entropy or pressure primitive variables are used, then the incompressible limit of the Navier-Stokes equations is well-defined, hence they are a suitable choice for obtaining a unified formulation. These two sets of variables are investigated in detail
Conformal Field Theory as Microscopic Dynamics of Incompressible Euler and Navier-Stokes Equations
We consider the hydrodynamics of relativistic conformal field theories at
finite temperature. We show that the limit of slow motions of the ideal
hydrodynamics leads to the non-relativistic incompressible Euler equation. For
viscous hydrodynamics we show that the limit of slow motions leads to the
non-relativistic incompressible Navier-Stokes equation. We explain the physical
reasons for the reduction and discuss the implications. We propose that
conformal field theories provide a fundamental microscopic viewpoint of the
equations and the dynamics governed by them.Comment: 4 page
Incompressible Limit of a Compressible Liquid Crystals System
This article is devoted to the study of the so-called incompressible limit
for solutions of the compressible liquid crystals system. We consider the
problem in the whole space and a bounded domain of
with Dirichlet boundary conditions. Here the number
of dimension or 3
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