Research in Nonlinear Partial Differential Equations and Bifurcation Theory

摘要

We prove a necessary condition and a sufficient condition for the existence of steady plane wave solutions to the Navier Stokes equations for a reacting gas. These solutions represent plane detonation waves, and converge to ZND detonation waves as the viscosity, heat conductivity, and species diffusion rates tend to zero. We assume that the Prandtl number is 3/4, but we permit arbitrary Lewis numbers. We make no assumption concerning the activation energy. We show that the stagnation enthalpy and the entropy flux are always monotone for such solutions, and that the mass density and pressure are nearly always not monotone, as predicted by the ZND theory. In certain parameter ranges, typically that of large diffusion, many of these waves have the appearance of a weak detonation followed by an inert shock wave. This confirms a phenomenon observed in numerical calculations and in a model system by Colella, Majda, and Roytburd.