Motion of a slightly compressible fluid.
TLDR
It is shown that the motion of a slightly compressible fluid is near that of an incompressible fluid, and the minimum of the potential energy function becomes sharper if the equation of state of the compressable fluid is changed so that the sound speed increases.Abstract:
We show that the motion of a slightly compressible fluid is near that of an incompressible fluid. That is, for a given initial velocity field, the motion of a compressible fluid with large sound speed is near to that of an idealized incompressible fluid. We consider the compressible fluid motion in Lagrangian coordinates and show that it can be defined by two functions giving the kinetic and potential energies. The minimal set for the potential energy is the configuration space of incompressible fluid motion. If the equation of state of the compressible fluid is changed so that the sound speed increases, the minimum of the potential energy function becomes sharper. The compressible fluid motion approaches a curve in the minimal set and this curve defines an incompressible fluid motion.read more
Citations
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References
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Groups of diffeomorphisms and the motion of an incompressible fluid
David G. Ebin,Jerrold E. Marsden +1 more
TL;DR: In this article, the authors studied the manifold structure of certain groups of diffeomorphisms, and used this structure to obtain sharp existence and uniqueness theorems for the classical equations for an incompressible viscous and non-viscous fluid on a compact C^∞ riemannian, oriented n-manifold, possibly with boundary.
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