In the equation,differential viscosity and the first normal stress function are defined to specify the rheological properties of non-Newtonian medium,flow factors are used to specify the effect of surface roughness.

In the equation,differential viscosity and the first normal stress difference function were defined to specify the rheological properties of non-Newtonian medium,squeeze item was used to specify the effect of dynamic load.

Comparison of bubble formation in Newtonian and non-Newtonian fluids;

The waviness were given by sinusoidal functions,and the non-Newtonian flow of the lubricant was described by the Ree-Eyring model.

Thus a mathematical model for the isothermal EHL with non-Newtonian lubrication of the elliptical contact was proposed, by taking into account the two surface velocities in the same and opposite directions or each at an arbitrary angle to the minor axis of the contact ellipse.

For well test of non-newtonian fluid , scholars inland and abroad has made a lot of study and acquired lots of results, but these results still can't solve well the practical problems on engineering because of the complexity of the permeability process, so it requires people to make deeper study.

In this paper, we consider a class of compressible non-Newtonian fluids in one-dimensional bounded intervals:with the initial and boundary conditionswhereρ, u andπdenote the unknown density, velocity and pressure, respectively.