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

Abstract

The aims of this paper are to discuss existence and uniqueness of local solutions for a class of nonNewtonian 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.

Global strong solutions for a class of compressible non-Newtonian fluids with vacuum

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