Subsonic Flows In Three-dimensional Semi-infinitely Long Nozzles With Largely-open Divergent Part

In this thesis, we study the existence, uniqueness and regularity of steady sub-sonic irrotational isentropic compressible flows in three-dimensional semi-infinitely long nozzles with largely open divergent part. Such nozzles consist of a cone with arbitrary open angle and a tube which is a cylinder near the inlet. The subsonic flow is described by a boundary value problem for a second order quasilinear equation of the velocity potential, which is the so called inviscid potential flow equation. First, we get a boundary value problem (called modified problem) for a uniformly elliptic equation by modifying the density function of the flows; Second, we use the direct methods of calculus of variations to prove the existence on the modified problem’s weak solution; Third, we prove the regularity of the weak solution by applying Moser iteration techniques and prove the decay of gradient of weak solution by scaling; Forth, we prove the uniqueness of weak solutions of finite energy; Finally, we illustrate that there is a critical value m0and the modified problem is subsonic and hence reduced to the original problem when the total mass flux is less than m0. So we proved the existence, uniqueness and regularity of the problem of subsonic flow.