On the equations of thin shock layer theory

The theory of high Mach number flows creating a thin layer between a shock wave and a delta wing surface rests on a certain functional equation or its associated differential one, both of which are nonstandard and the existence of solutions cannot be guaranteed. There exists a free parameter within these equations in the form of the shape of the wing, about which we wish to obtain necessary conditions for a thin shock layer to exist. We get some direct estimates in terms of bounds on the side flow at the initial condition, as well as some indirect ones related to the regularity of the shock wave, which is itself linked to the energy of the flow. •The equations of thin shock layer theory are detailed.•A mathematical study of them is performed.•Conditions for the existence of solutions depending on the wing are found.•Conditions for the existence of solutions depending on the shock are found.