The Navier–Stokes hypersonic weak-interaction theory is presented for the flow of a viscous, heat-conducting, compressible fluid past a very slender axisymmetric body, when the ratio of the radius of the body to the radial thickness of the viscous region, produced and supported by the body, is much less than unity. The fluid is assumed to be a perfect gas having constant specific heats, a constant Prandtl number of order unity, and viscosity coefficients varying as a power of the absolute temperature. Solutions are studied for the free-stream Mach number, the free-stream Reynolds number based on the axial length of the body, and the reciprocal of the weak-interaction parameter much greater than unity.

It is shown that, for the viscosity-temperature exponent ω less than 1, seven distinct layers span the region between the shock wave and the body, which is of arbitrary shape. The leading approximations for the behaviour of the flow in these seven layers are analyzed, and the restrictions imposed on the theory are obtained.