We study the uniformregularity 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., 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 C1 continuous.
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