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In this paper, we establish the first rigorous mathematical global result onthe validation of the hypersonic similarity, which is also called theMach-number independence principle, for the two dimensional steady potentialflow. The hypersonic similarity is equivalent to the Van Dyke's similaritytheory, that if the hypersonic similarity parameter $K$ is fixed, the shocksolution structures (after scaling) are consistent, when the Mach number of theflow is sufficiently large. One of the difficulty is that after scaling, thesolutions are usually of large data since the perturbation of the hypersonicflow is usually not small related to the sonic speed. In order to make it, wefirst employ the modified Glimm scheme to construct the approximate solutionswith large data and find fine structure of the elementary wave curves to obtainthe global existence of entropy solutions with large data, for fixed $K$ andsufficiently large Mach number of the incoming flow $M_{\infty}$. Finally, wefurther show that for a fixed hypersonic similarity parameter $K$, if the Machnumber $M_{\infty}\rightarrow\infty$, the solutions obtained above approach tothe solution of the corresponding initial-boundary value problem of thehypersonic small-disturbance equations. Therefore, the Van Dyke's similaritytheory is first verified rigorously.

Hypersonic Similarity for the Two Dimensional Steady Potential Flow with Large Data