Smooth subsonic combustion flows in a cylindrical nozzle

This paper concerns the well-posedness of subsonic combustion flows in a cylindrical nozzle. We establish the existence and uniqueness of three-dimensional smooth subsonic flows to the steady Zeldovich–von Neumann–Döring combustion equations by prescribing the Bernoulli’s quantity, the entropy, the fraction of unburned gas and the tangential velocity at the entrance and the pressure at the exit. The problem is formulated as a nonlinear boundary value problem for a hyperbolic-elliptic mixed system. The main difficulty is that all the physical quantities are coupled with each other due to the combustion process. One of the key points in the analysis is to utilize the deformation-curl decomposition to deal with the hyperbolic and elliptic modes. Another one is to solve the deformation-curl system for the velocity field with mixed boundary conditions.