标题： 三维稳态势流在球坐标系中的比较原理 显示英文标题

标题： Comparison principles for 3-D steady potential flow in spherical coordinates

摘要： 在本文中，我们考虑可压缩气体的三维定常势流，其压力满足$p'(\rho)=\rho^{\gamma-1}$，其中$\rho$是密度，$\gamma\geq-1$是一个常数。 在球坐标系中，势方程在单位球体内为混合类型。 我们建立了该方程椭圆解的强比较原理。 与经典情况的主要区别在于，该方程的系数完全依赖于势函数本身。 我们通过对方程自身结构的充分分析克服了这一困难，并最终得出了结果。 此处得到的结果可以应用于三角翼超音速流动问题及其他与气体动力学相关的问题。 显示英文摘要

摘要： In this paper, we consider the 3-D steady potential flow for a compressible gas with pressure satisfying $p'(\rho)=\rho^{\gamma-1}$, where $\rho$ is the density and $\gamma\geq-1$ is a constant. In spherical coordinates, the potential equation is of mixed type in the unit sphere. We establish a strong comparison principle for elliptic solutions of the equation. The main difference from the classical case is that the coefficients of this equation depend fully on the potential function itself. We overcome this difficulty by the sufficient analysis on the structure of the equation itself, and finally derive the result. The result obtained here can be applied to the problem of supersonic flow over a delta wing and other problems related to gas dynamics.