Thermodynamic analysis shows that for flights with velocities exceeding six sound velocities, it is required to burn fuel not in a subsonic but in a supersonic flow. The aim of this work is to investigate the possibility of creating a stationary combustion front in a supersonic flow by igniting the mixture with an attached microwave discharge. Discharges are created on the resonator by means of a pulsed source of quasi-optical microwave radiation. This method of initiation is one or two orders of magnitude more economical than other known methods of plasma ignition and combustion stabilization. A numerical evaluation and comparison with experiment of the propagation velocity of a subcritical streamer discharge in a stationary medium and in a supersonic drifting flow are performed. Experiments have been conducted to ignite a flat flow of propane-air mixture, as well as ignition of the propane stream fed into the airflow, which simulates the operation of the fuel injector. In all cases, the experiments confirmed a steady fuel combustion, which was controlled by the temperature measurements with a thermocouple.