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In this paper we prove existence, uniqueness and regularity of certainperturbed (subsonic--supersonic) transonic potential flows in a two-dimensionalRiemannian manifold with "convergent-divergent" metric, which is an approximatemodel of the de Laval nozzle in aerodynamics. The result indicates thattransonic flows obtained by quasi-one-dimensional flow model in fluid dynamicsare stable with respect to the perturbation of the velocity potential functionat the entry (i.e., tangential velocity along the entry) of the nozzle. Theproof is based upon linear theory of elliptic-hyperbolic mixed type equationsin physical space and a nonlinear iteration method.

Transonic Potential Flows in A Convergent--Divergent Approximate Nozzle