Computational Fluid Dynamics (CFD) was used to investigate the flow in a rotating detonation engine (RDE) with ideal and slot injection of H₂-air at stoichiometric conditions. A detailed kinetic mechanism was used to show that a stable, grid independent, rotating detonation traveling at the correct speed could be established for ideal injection. Stable rotating detonation was not sustained when slot injectors were used with an area ratio of 0.2. Numerical experiments showed that a higher area ratio is required to establish a single rotating detonation when using a realistic kinetics model. A one-step kinetic model with longer induction time was used to establish a stable rotating detonation wave within the engine for injectors with an area ratio of 0.2. These studies point to issues with the presence of hot burned gas in the head-end of the RDE affecting the stability of RDE operation.