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In this paper, the one-dimensional compressible Navier-Stokes system withouter pressure boundary conditions is investigated. Under some suitableassumptions, we prove that the specific volume and the temperature are boundedfrom below and above independently of time, and then give the local and globalexistence of strong solutions. Furthermore, we also obtain the convergence ofthe global strong solution to a stationary state and the nonlinearly stabilityof its convergence. It is worth noticing that all the assumptions imposed onthe initial data are the same as Takeyuki Nagasawa [Japan.J.Appl.Math.(1988)].Therefore, our work can be regarded as an improvement of the results ofTakeyuki.

Nonlinearly stability of solutions on the outer Pressure Problem of Compressible Navier-Stokes System with Temperature-Dependent Heat Conductivity