ASYMPTOTIC ANALYSIS OF AN ISOTHERMAL GAS FLOW THROUGH A LONG OR THIN PIPE

Abstract

In this paper we study the compressible stationary isothermal flow through a thin (or long) straight pipe. Starting from the compressible Stokes system, via rigorous asymptotic analysis, as the pipe's thickness tends to zero, we obtain the 1D model describing the effective behavior of the flow. The uniqueness of the solution for such model is proved, if the first component of the function g, appearing on the right-hand side of the system, does not change its sign. If it does change the sign, an example of non-uniqueness of the solution is given.