Self-similar solutions of the compressible flow in one-space dimension
Summary: For the isentropic compressible fluids in one-space dimension, we prove that the Navier-Stokes equations with density-dependent viscosity have neither forward nor backward self-similar strong solutions with finite kinetic energy. Moreover, we obtain the same result for the nonisentropic compressible gas flow, that is, for the fluid dynamics of the Navier-Stokes equations coupled with a transport equation of entropy. These results generalize those in \textit{Z. Guo} and \textit{S. Jiang}'s work [IMA J. Appl. Math. 71, No. 5, 658--669 (2006; Zbl 1112.76059)] where the one-dimensional compressible fluids with constant viscosity are considered.
scientific article; zbMATH DE number 6950550