article

Title: On subsonic Euler flows with stagnation points in two-dimensional nozzles

Authors: Chunjing Xie and Lili Du

Issue: Volume 63 (2014), Issue 5, 1499-1523

Abstract:

$In this paper, we study the existence and structural stability of steady compressible subsonic flows with stagnation points and non-zero vorticity through two-dimensional infinitely long nozzles which have finitely many corners on the nozzle walls. An important observation is that the flows in these nozzles do not have stagnation points except at the corner points. This makes the stream function formulation an efficient way to solve the hyperbolic equation in the Euler system. We also show that subsonic flows are structurally stable in the sense that the subsonic flows are stable under small $C^{1,\alpha}$-smooth perturbations for the nozzle walls. Our analysis uses the regularity theory for quasilinear elliptic equations in both regular and irregular domains, the analysis developed in [C.J. Xie and Z.P. Xin, \textit{Existence of global steady subsonic Euler flows through infinitely long nozzles}, SIAM J. Math. Anal. \textbf{42} (2010), no. 2, 751--784] for the stream-function formulation for the Euler system, and a particular choice of smooth transformations between non-smooth domains.$