Steady subsonic potential flows through infinite multi-dimensional largely-open nozzles

Abstract

We proved existence, regularity and uniqueness of steady subsonic potential flows in n-dimensional (n ≥ 3) infinite nozzles with largely-open convergent and divergent parts when the total mass flux is less than a certain value. Such nozzles consist of two cones with arbitrary open angles and an arbitrary smooth bounded tubular part. The existence of a weak solution is proved by applying the direct method of calculus of variation to a carefully chosen functional defined on a Hilbert space based upon Hardy inequality. Holder gradient regularity of weak solution is shown by using Moser iteration to quasilinear elliptic equations in divergence form. Also, the obtained solution is unique in the class of functions with finite kinetic energy by modulo a constant.