研究二维轴对称压差方程组活塞问题局部解的存在性.首先，利用轴对称的特点，选用合适的变量将原问题转化为一维问题.然后，利用Taylor展开的方法构造原问题的一个N阶近似解.进而以此近似解作为迭代的首项，通过Newton迭代法，并利用对相应线性问题所作的能量估计，最终证明其活塞问题激波解的局部存在性.

In this paper, we consider the existence of local solutions to a 2-dimensional axially-symmetrical piston problem of pressure-gradient equations. As the problem is axially-symmetric, proper variables first are selected to transform the original problem into a 1-dimensional problem. By Taylor expansion, we construct an N-ordered approximate solution used as the first term in the Newton iterative method. With the Newton iteration and the energy estimation, we show the local existence of the shock front solution to the problem.