Shock waves in three-dimensional transonic flow with weak spatial heat release

The presence or absence of shock waves in the case of weak 3D heat release to homogeneous uniform transonic gas flow is analyzed. It is well known that shock waves can exist in a steady-state flow in the 2D case for a small transonic similarity number. It is shown that in the main approximation, shock waves are absent in the axisymmetric and 3D versions. In the next approximation, in which the logarithm factor of a small parameter is absent, shock waves can exist.