On the existence and asymptotical behaviour of a steady flow of a viscous barotropic gas in a pipe
The authors discuss the existence, uniqueness and asymptotic behaviour of steady three-dimensional flows of an isothermal viscous gas in channels with finite cross-sections at infinity, i.e. as \(|x_3|\to\infty\). This problem is studied first for Poisson-Stokes equations with an additional ``flux'' condition, and then for a control problem of Navier-Stokes type. The proof is based on the investigation of an auxiliary linear problem with subsequent iterations to the nonlinear case.
channels with finite cross-sections at infinity
scientific article; zbMATH DE number 1383212
scientific article