Groups of diffeomorphisms and the solution of the classical Euler equations for a perfect fluid

This chapter presents the laws of motion of an ensemble of point masses forming a solid body whose shape is invariant, or a fluid whose shape can vary with time. It argues that an ensemble of point masses constitutes a solid if the distances between the points can be assumed constant. The chapter then provides examples of the motions of a solid. Finally, it demonstrates the Euler equations of fluid motion. Here, it states that a perfect fluid is characterized by its (inertial) mass density ρ‎(t, xⁱ), its pressure p(t, xⁱ) which phenomenologically describes its internal collisions, and a velocity field v(t, xⁱ) giving its velocity at xⁱ at time t.

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Groups of diffeomorphisms of $R^n$ and the flow of a perfect fluid

Bulletin of the American Mathematical Society ◽

10.1090/s0002-9904-1975-13713-x ◽

1975 ◽

Vol 81 (1) ◽

pp. 205-209 ◽

Cited By ~ 2

Author(s):

Murray Cantor

Keyword(s):

Perfect Fluid ◽

Groups Of Diffeomorphisms

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Classical solutions to the relativistic Euler equations for a linearly degenerate equation of state

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891617500187 ◽

2017 ◽

Vol 14 (03) ◽

pp. 535-563 ◽

Cited By ~ 4

Author(s):

Changhua Wei

Keyword(s):

Initial Data ◽

Global Existence ◽

Classical Solution ◽

Perfect Fluid ◽

Euler Equations ◽

Chaplygin Gas ◽

Classical Solutions ◽

Relativistic Euler Equations ◽

Stiff Matter ◽

Linearly Degenerate

We are concerned with the global existence and blowup of the classical solutions to the Cauchy problem of one-dimensional isentropic relativistic Euler equations (Chaplygin gas, pressureless perfect fluid and stiff matter) with linearly degenerate characteristics. We at first derive the exact representation formula for all the fluids by the property of linearly degenerate. Then for the Chaplygin gas and the pressureless perfect fluid, we give a classification of the initial data that leads to the global existence and the blowup of the classical solution, respectively. We construct, especially, a class of initial data that contributes to the formation of “cusp-type” singularity and study the evolution of the solution after blowup by introducing a weak solution called delta shock wave. At last, for the stiff matter, we show that this system is indeed a linear system and prove the global existence of the classical solution to this fluid.

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ON A PERFECT FLUID KÂ¨ AHLER SPACETIME

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v12i3.44 ◽

2016 ◽

Vol 12 (3) ◽

pp. 4350-4355

Author(s):

VIBHA SRIVASTAVA ◽

P. N. PANDEY

Keyword(s):

Field Equation ◽

Perfect Fluid ◽

Sectional Curvature ◽

Einstein Field Equation ◽

Cosmological Term ◽

Conformal Killing ◽

Killing Vectors ◽

Projectively Flat ◽

Conformal Killing Vectors

The object of the present paper is to study a perfect fluid KÂ¨ahlerspacetime. A perfect fluid KÂ¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid KÂ¨ahler spacetime have been obtained. Dust model for perfect fluid KÂ¨ahler spacetime has also been studied.

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