Two Models Of 1-D Compressible Euler Equations

In the study of physics and other application areas, mostly, the problem can be reduced to the mathematical problem. As an important system in gas dynamic and fluid mechanics etc., compressible Euler systems is one of hot topics in mathematics and physics.In this paper, we will give two models of 1-D compressible Euler equations:1-D Chap-lygin gas in non-isentropic case and 1-D compressible Euler equations with geometrical struc-ture. Firstly, we consider Cauchy problem for the 1-D Chaplygin gas in non-isentropic case, which the adiabatic index is γ= - 1. Under the appropriate assumptions, using the character-istic theory and Gronwall’s inequality, we obtain the global existence to the classical solutions with uniform bounds. Secondly, we consider the 1-D compressible Euler equations with geo-metrical structure and the adiabatic index y= 3, we also get the uniform L∞ bound independent of T.