Existence and uniqueness of solutions for a class of non-Newtonian fluids with singularity and vacuum

The aims of this paper are to discuss existence and uniqueness of local solutions for a class of non-Newtonian fluids with singularity and vacuum in one-dimensional bounded intervals. There are two important points in this paper, one is that we allow the initial vacuum; another one is that the viscosity term of momentum equation is with singularity and fully nonlinearity.