Solvability of a Boundary Value Problem for Transonic Flow in a Nozzle

Abstract

A nonlinear perturbation problem for steady two-dimensional inviscid transonic flow in a nozzle is studied. The existence of a smooth solution to the problem is proved under the condition of positive acceleration of the given flow. The proof involves the method of singular perturbations for solving a linear problem associated with the nonlinear one. The technique for obtaining a priori estimates is simpler than that used in previous papers.