The Global Entropy Solutions To The Cauchy Problem Of The Isentropic Relativistic Euler Equations With A Class Of Large Initial Data

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 the average speed of baryon is close to the light speed, the relativistic effect is not ignored. At this point the classical equations of hydrodynamics no longer set up, and should be replaced by relativistic hydrodynamics (cf [43, 44, 45]). Relativistic fluid dynamics are an effect research tool in astrophysics, plasma physics, nuclear physics and so on. Einstein proposed the task of researching the fluid movement when he created the theory of the relativity.But the real research for relativistic hydrodynamics equations was very late. Until 1970, the first international seminar relativistic hydrodynamics was held. Since then, because of plasma physics and nuclear physics requirements for the development, the research of the relativistic hydrodynamics equations has made significant progress. In fact,the relativistic hydrodynamics equations system is a good mathematical model of high-energy astrophysics plasma. Now, it is used in analysis of nuclear physics' heavy ion reaction. However, as different in mathematical problems, the study is not mature in mathematics about relativistic hydrodynamics. Mathematician at present mainly study the exist of solution and the state of solution in the one-dimensional case of certain special circumstances. Further, as the convergence of numerical scheme is great depend on the support of its mathematical structure of understanding. We research the relativistic hydrodynamics equations will contribute to the relativistic hydrodynamics' numerical analysis and calculation. In addition, we note that the Newton limit of the relativistic hydrodynamics equations is the classical compressible fluid Euler equations system. This is one of the motives that we research the relativistic hydrodynamics equations.The main research of this paper is the global entropy existence of the isentropy relativistic Euler equation's cauchy problem with a large initial data. Since 1965, the Gelimm's book has come out(cf [18]). The solution of general conservation laws equation with the small initial data has been solved. This theorem generally requirements that the solution's oscillation or the total variance is enough small. But this paper may prove that if the initial data are satisfy the initial conditions, we can get the cauchy problem's global solution using Glimm difference scheme and we don't need the solution's oscillation or the total variance is enough small.