Existence Of The Global H(o|¨)lder Solutions For Isentropic Gas Dynamics With Negative Pressure

There have been so many papers studying the global Holder solutions of the isntropic gas dynamic with positive pressure and solutions or uniqueness for pressureless type Cauchy problems. Here in this paper, we are going to discuss the the global Holder solutions of the isntropic gas dynamic with negative pressure in Euler coordinates. with initial datas: Where P(p)=γργ, and-1≤γ<0, ρ>0. The method here we use is a method called vanishing viscosity. And the structure of this paper is organized as followed:In chapter1, we talk a little bit the historical work and current status of the nonlinear conservative equations. Later we show the physical background and benefits of this paper’s topic. Then we go forward to introduce the basic thoeries on the nonlinear conservative equations.In chapter2, we firstly get the transformation of the original system by Riemann Variants. Then a priori estimate for the solutions of the reformed system can be gained under some restrictions on initials.In chaper3, we will get the right weak solution for the origianl system with the help of the priori estimate from chapter2, and give the proof in the end.In chapter4, we make some consolutions and prospect of this topic.