Existence of solutions to the transonic pressure gradient equations of the compressible euler equations in elliptic Regions

Abstract

We establish the existence of a smooth solution in tis elliptic region in the self—similar plane to the pressure—gradient system arisen from the wave—particle splitting of the two—dimensional compressible Euler system of equations. The pressure—gradient system takes the form Here (u,v) is the velocity, ρ is the density which is independent of time resulted from the splitting procedurep is the pressure, and is the energy. The natural (parabolically degenerate) boundary value is used.