Abstract We formulate a mathematical problem on hypersonic-limit of three-dimensional steady uniform non-isentropic compressible Euler flows of polytropic gases passing a straight cone with arbitrary cross-section and attacking angle, which is to study Radon measure solutions of a nonlinear hyperbolic system of conservation laws on the unit 2-sphere. The construction of a measure solution with density containing Dirac measures supported on the surface of the cone is reduced to find a regular periodic solution of highly nonlinear and singular ordinary differential equations (ODE). For a circular cone with zero attacking angle, we then proved the Newton's sine-squared law by obtaining such a measure solution. This provides a mathematical foundation for the Newton's theory of pressure distribution on three-dimensional bodies in hypersonic flows.

中文翻译：

---

高超声速极限锥形流和牛顿正弦平方定律的稳定可压缩欧拉方程的氡测量解

摘要 我们提出了多方气体通过任意截面和攻角的直锥体的三维稳态均匀非等熵可压缩欧拉流的高超声速极限数学问题，研究非线性双曲系统的氡测度解。单位 2 球体上的守恒定律。构造具有密度包含在锥体表面上的狄拉克测度的测度解，以找到高度非线性和奇异常微分方程 (ODE) 的正则周期解。对于攻角为零的圆锥，我们通过得到这样的测度解，证明了牛顿正弦平方定律。这为牛顿法提供了数学基础