The Newtonian Limit Of The Global Entropy Solutions To The Cauchy Problem Of The Isentropic Relativistic Euler Equations

When we research the fluids movement,the classical hydrodynamics is in the dominant position if the speed of fluids or the baryon is less than the light speed; When the speed of fluids or average speed of baryon is close to the light speed,the rel-ativistic effect is not ignored.At the classical this point the classical equations of hydrodynamics.In this article, we will discuss the limit problem of the entropy solution of the isentropic relativistic Euler equations.In the article [42], the authors discussed the limit problem of the isentropic relativistic Euler equations with the equation of state p=k2ρ, which contain two equations describing the conservation of the particle numbers and momentum. In this article we still discuss this equations but with different equation of state p k2ργ,γ＞1. In order to obtain the limit of global entropy solution of the relativistic Euler equations, we will estimate the total variation of the approximate solution obtained by Glimm format. We will prove that the estimation is independent of the speed of light c(c≥co,co is a positive constant) in order that we can get a convergent sequence{ck}. Let k→+∞, with the compactness of the convergent sequence we can prove that the limit of the entropy solution of the relativistic Euler equations is just the solution of non-relativistic Euler equations.In addition,we note that the Newtonian limit of the relativistic hydrodynam-ics equations is the classical compressible fluid Euler equations.This is one of the motives that we research relativistic hydrodynamics equations.