A Class Of Compressible Non-newtonian Fluid With Self-gravitational Potential

Fluid mechanics is an important branch of mechanics,which studies the mechanical motion law in fluid.With the progress of society and the development of science and technology,there exist a large number of non-Newtonian fluids in people’s daily life.In recent years,more and more attention has been paid to the important properties of non-Newtonian fluids.Non-Newtonian fluid refers to the fluid which does not satisfy the linear relationship between shear stress and shear deformation rate.It mainly follows the conservation of mass and the conservation of momentum.Non-Newtonian fluid mechanics is widely used in life,environmental protection,science and technology and engineering.In this thesis,two kinds of non-Newtonian equations with self-gravitational potential are studied,and the existence and uniqueness of the corresponding strong solutions are discussed.The main contents are as follows:The first part of this thesis deals with the initial boundary value problem for a class of compressible shear thinning fluid with self-gravity potential.It is proved that the initial boundary value problem has a unique local strong solution without external force.Firstly,the approximate solution is constructed by using the iterative method and the auxiliary function is set up to overcome the singularity of the momentum conservation equation and the strong coupling of the equations,and finally,the existence and uniqueness of the local strong solution of this kind of problem is proved.The second part of this thesis is concerned with the initial boundary value problem of a compressible shear thickening fluid with a self-gravitational potential.Due to the strong nonlinearity and strong coupling of the equation,on the basis of the mass conservation and momentum conservation theorem,the influence of the approximate solution on the equations is overcome through the consistent estimation of the approximate solution,and the existence and uniqueness of the local strong solution of this kind of problem is finally proved.