Contact discontinuities for 3-D axisymmetric flows with nonzero swirl

In this paper, we prove the existence and far-field behavior of an axisymmetric solution $(\rho ,\mathbf{u},p)$ to the steady Euler system in an infinitely long cylindrical nozzle with a perturbed wall $r=R(x_1)$, containing a contact discontinuity $r=g_D(x_1)$. The background flow carries a nonzero swirl component ${\beta }_0{\mathbf{e}}_{\theta }$, where ${\beta }_0$ is not necessarily small. Consequently, the background entropy, Bernoulli function, and angular momentum density depend on the radial variable, and their radial derivatives are not necessarily small.