“…In our previous studies [10,12,13,14], we considered rarefied monatomic gas between two coaxial unconfined cylinders (one dimensional, axisymmetric problem) by using a statistical method -Direct Simulation Monte Carlo (DSMC) and the Navier-Stokes-Fourier equations numerical solving. The present paper is a continuation of a study of Taylor-Couette flow between cylinders of finite length [21,22] where we consider the Taylor-Couette flow (two dimensional, axisymmetric problem) in rarefied gas between two concentric stationary cylinders with final length. The state of the gas is studied over a long time period close to establishing a steady state in [21], while in [22] is studied the initial moment of occurrence and reflection of the wave from the inner cylinder, when the cylinder temperature suddenly increases.…”