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In this paper, the steady inviscid flows with radial symmetry for theisothermal Euler system are studied in an annulus. We present a completeclassification of transonic radially symmetric flow patterns in term ofphysical boundary conditions at the inner and outer circle. By solving the oneside boundary problem, we obtain that there exist accelerating or deceleratingsmooth transonic flows in an annulus. Moreover, the structural stability ofthese smooth symmetric transonic flows with nonzero angular velocity arefurther investigated. Furthermore, we examine the transonic solutions withshocks as well via prescribing suitable boundary conditions on the inner andouter circle.

Smooth Symmetric Transonic Isothermal Flows with Nonzero Angular Velocity