Existence And Uniqueness Of Strong Solutions For Compressible Non-newtonian Ellis Fluids In One-Dimension With Vacuum

In the paper, we consider the Ellis system: with the initial and boundary conditions: where g, u and P denote the unknown density,velocity,and pressure,respectively and the motion of the fluid is driven by an external force f,the initial po> 0,p> 2,μ0> 0,μ1> 0 satisfy the following regularity conditions p> 2 is given constants an T= [0,1].This paper is to discuss existence and uniqueness of the solution for a class of non-Newtonian fluids with vacuum in one-dimensional bounded intervals, We hope our re-search results can enrich the compressible non-Newtonian fluids theory, but also can pro-mote the related problems.