1. School of Mathematics and Statistic, Shandong University, Weihai, P. 2. R. 3. China;4. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, P. 
Abstract:
The paper is devoted to the existence and uniqueness of local solutions for the density‐dependent non‐Newtonian compressible fluids with vacuum in one‐dimensional bounded intervals. The important points in this paper are that the initial density may vanish in an open subset and the viscosity coefficient is nonlinearly dependent of density and shear rate.