The structure of solutions near a sonic line in gas dynamics via the pressure gradient equation

A key issue in gas dynamics in two space dimensions is the regularity of solutions near a sonic curve. We build a large class of regular solutions with given boundary conditions on the sonic line. The modeling equation is the pressure gradient equation, which is the same as Euler system when the parameters of the gas are pushed to certain extreme. We use a novel set of coordinates, involving both the space–time and state variables, to split regular terms from singular terms in the analysis.