Global strong solutions of a class of non-Newtonian fluids with small initial energy.

Abstract In this paper, we are concerned with an initial–boundary value problem for a class of non-Newtonian fluids. The viscosity term of momentum equation possesses singularity and nonlinearity, and the initial vacuum is allowed. The main feature which distinguishes this paper from other related works lies in the fact that we study the global strong solution of the compressible non-Newtonian fluids with singularity and vacuum in one-dimensional bounded intervals, and show that there exists a unique global-in-time strong solution to the problem while the initial energy is small. [ABSTRACT FROM AUTHOR]