Flow in ducts with varying cross-sectional area and friction

Abstract

In this paper, we study the non-isentropic compressible Euler equations in ducts with varying cross-sectional area and friction. We analyze the combined effect of cross-sectional area and friction subtly and investigate the motion trend of the corresponding steady flow along ducts. Moreover, for the time-dependent system, when the boundary perturbations are temporal-periodical, we can utilize an energy function and Gronwall's inequality to demonstrate that the smooth supersonic solution is a temporal periodic solution, after a certain start-up time, possessing the same period as the boundary conditions. The semi-global existence of a C 1 solution to the mixed initial-boundary value problem is used in the proof.