Abstract:

We obtained a blowup criterion for strong solutions to a class of compressible non-Newtonian fluids just in terms of the derivative of the velocity using the proof of contradiction. In other words, if the derivative of the velocity remains bounded as time t approaches to the critical time, a local strong solution can be continued globally in time. In addition, the initial vacuum states are allowed in our cases.

Key words: blowup criterion, compressible nonNewtonian fluids, vacuum, strong solutions