### Electronic Research Archive

2020, Issue 1: 47-66. doi: 10.3934/era.2020004
Special Issues

# The existence of solutions for a shear thinning compressible non-Newtonian models

• Received: 01 September 2019 Revised: 01 November 2019
• Primary: 76A05, 76N10

• This paper is concerned with the initial boundary value problem for a shear thinning fluid-particle interaction non-Newtonian model with vacuum. The viscosity term of the fluid and the non-Newtonian gravitational force are fully nonlinear. Under Dirichlet boundary for velocity and the no-flux condition for density of particles, the existence and uniqueness of strong solutions is investigated in one dimensional bounded intervals.

Citation: Yukun Song, Yang Chen, Jun Yan, Shuai Chen. The existence of solutions for a shear thinning compressible non-Newtonian models[J]. Electronic Research Archive, 2020, 28(1): 47-66. doi: 10.3934/era.2020004

### Related Papers:

• This paper is concerned with the initial boundary value problem for a shear thinning fluid-particle interaction non-Newtonian model with vacuum. The viscosity term of the fluid and the non-Newtonian gravitational force are fully nonlinear. Under Dirichlet boundary for velocity and the no-flux condition for density of particles, the existence and uniqueness of strong solutions is investigated in one dimensional bounded intervals.

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