86,595 research outputs found

    Incompressible Limit of Solutions of Multidimensional Steady Compressible Euler Equations

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    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

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    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

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    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

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    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 RN\mathbb{R}^{\mathbb{N}} and a bounded domain of RN\mathbb{R}^{\mathbb{N}} with Dirichlet boundary conditions. Here the number of dimension N=2\mathbb{N}=2 or 3
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