Self-similar solutions of the compressible flow in one-space dimension

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 guo and jiang's work (2006) where the one-dimensional compressible fluids with constant viscosity are considered. © 2013 tailong li et al.