Abstract: We considered a class of compressible nonNewtonian fluid equations in onedimensional bounded interval. Under the conditions that the external force term was relatively small, a priori estimates were given by the method of hypothesis closure, weighting and energy estimates. We proved the existence and uniqueness of the global strong solutions and gave the long time behavior of the solution.

Key words: non-Newtonian fluid, strong solution, a priori estimate, long time behavior