The regularity of semi-hyperbolic patches at sonic lines for the pressure gradient equation in gas dynamics Qin WangYuxi Zheng 35L6535J7035R352-D Riemann problembootstrapcharacteristic decompositionsmoothnesssonic line. We study the uniform regularity of semi-hyperbolic patches of self-similar solutions near sonic lines to a general Riemann problem for the pressure gradient equation. This type of solution, in which one family of characteristics starts on a sonic line and ends on a transonic shock wave, is common for the Riemann problems for the Euler system in two space dimensions. The global existence of smooth solutions was established in Song and Zheng [Disc.\ Cont.\ Dyna.\ Syst., \textbf{24} (2009),1365-1380], but the smoothness near the sonic lines is not clear. We establish that the smooth solutions are uniformly smooth up to their sonic boundaries, and that the sonic lines are $C^1$ continuous. Indiana University Mathematics Journal 2014 text pdf 10.1512/iumj.2014.63.5244 10.1512/iumj.2014.63.5244 en Indiana Univ. Math. J. 63 (2014) 385 - 402 state-of-the-art mathematics http://iumj.org/access/