On a supersonic-sonic patch arising from the frankl problem in transonic flows

<p style="text-indent:20px;">We construct a supersonic-sonic smooth patch solution for the two dimensional steady Euler equations in gas dynamics. This is extracted from Frankl problem study of transonic flow with local supersonic bubble over an airfoil. Based on methodology characteristic decompositions, we establish global existence and regularity solutions partial hodograph coordinate system terms angle variables. The original solved by transforming plane back to that physical plane. Moreover, uniform associated sonic curve are also verified.</p>