压差方程整体解的存在性

The Existence of Global Solutions to a Class of Pressure-Gradient Equations

利用改进的Glimm格式讨论了压差方程整体解的存在性.通过研究压差方程Riemann不变量的性质来研究波的性质,证明了随着左状态的改变右状态集合组成的激波曲线满足Diperna条件,再利用Glimm格式构造近似解,在Riemann问题的解的变差由Riemann不变量控制,最后得到整体解的存在性.

In this paper,by using the improved Glimm scheme,the existence of the global solutions to a class of Pressure-Gradient equations is discussed.By studying the properties of Riemann invariants of the Pressure-Gradient equation,the properties of the wave are studied.It is proved that the shock curve composed of the right state set with the change of the left state satisfies the diperna condition.The approximate solution is constructed by using Glimm scheme.The variation of the solution of Riemann problem is controlled by Riemann invariant.Finally,the existence of global solution is obtained.