Abstract
This paper deals with a mathematical fluid-particle interaction model used to describing the evolution of particles dispersed in a viscous compressible non-Newtonian fluid. It is proved that the initial boundary value problems with vacuum admits a unique local strong solution in the dimensional case. The strong nonlinearity of the system brings us difficulties due to the fact that the viscosity term and non-Newtonian gravitational potential term are fully nonlinear.
Highlights
This paper deals with a mathematical fluid-particle interaction model used to describing the evolution of particles dispersed in a viscous compressible non-Newtonian fluid
It is proved that the initial boundary value problems with vacuum admits a unique local strong solution in the dimensional case
Fluid-particle interaction model arises in many practical applications in science and engineering [1,2,3,4] and is of primarily importance in the sedimentation analysis of disperse suspensions of particles in fluids
Summary
Fluid-particle interaction model arises in many practical applications in science and engineering [1,2,3,4] and is of primarily importance in the sedimentation analysis of disperse suspensions of particles in fluids. The friction force is assumed to follow the Stokes law and is proportional to the relative velocity of the fluid and the particles given by ξ − uε(t, x). Followed by the Ladyzhenskaya model, in this paper, we investigate the compressible non-Newtonian fluid-particle interaction model in one-dimensional case, system (8) changes to be ρt + (ρu)x = 0,. There seems very few mathematical results for the case of the fluid-particle interaction model systems with non-Newtonian gravitational potential, even in dimension one. The existence results to problem (14)-(16) when p, q > 2 which describes the motion of the compressible viscous isentropic gas flow is driven by a non-Newtonian gravitational force is still open up to now.
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