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For the three-dimensional steady non-isentropic compressible Euler systemwith friction, we show existence of a class of symmetric subsonic, supersonicand transonic-shock solutions in a straight duct with constant square-section.Such flows are called Fanno flow in engineering. We formulate a boundary valueproblem for subsonic flows, and study their stability under multidimensionalsmall perturbations of boundary conditions. Since the subsonic Euler system isof elliptic-hyperbolic composite-mixed type, this is achieved by using theframework established in [L. Liu; G. Xu; H. Yuan: Stability of sphericallysymmetric subsonic flows and transonic shocks under multidimensionalperturbations. Adv. Math. 291 (2016), 696--757], and establishing an iterationscheme, which involves solving a second order nonlocal elliptic equation.

Subsonic flows passing a duct for three-dimensional steady compressible Euler system with friction