论文标题
Chaplygin气体的超音速流经三角洲翼
Supersonic flow of Chaplygin gas past a delta wing
论文作者
论文摘要
我们考虑了三角洲机翼的超音速流量的问题，其冲击波或稀疏波在领先的边缘附着。研究的流量由三维稳定的Euler系统描述。在圆锥形坐标中，可以将此问题重新归类为混合类型非线性方程的边界价值问题。该方程的类型完全取决于问题本身的解决方案，因此无法事先确定。我们通过建立关键的Lipschitz估计来克服困难，并最终通过连续性方法证明解决方案的独特存在。
We consider the problem of supersonic flow of a Chaplygin gas past a delta wing with a shock or rarefaction wave attached to the leading edges. The flow under study is described by the three-dimensional steady Euler system. In conical coordinates, this problem can be reformulated as a boundary value problem for a nonlinear equation of mixed type. The type of this equation depends fully on the solutions of the problem itself, and thus it cannot be determined in advance. We overcome the difficulty by establishing a crucial Lipschitz estimate, and finally prove the unique existence of the solution via the method of continuity.
