The strong solutions for a class of fluid-particle interaction non-Newtonian models

Abstract

The aim of this paper is to discuss the existence and uniqueness for a class of fluid-particle interaction non-Newtonian models which describe the evolution of particles dispersed in a viscous compressible non-Newtonian fluid. The strong nonlinearity of the system and the singularity of the viscosity term bring about difficulties. Also, we admit an initial vacuum.

Strong Solutions for the Fluid-Particle Interaction Model with Non-Newtonian Potential

“…As to the non-Newtonian fluids, there has been much research both theoretically and experimentally, see ( [15][16][17][18][19][20][21][22][23]). Indeed, we have investigated the existence results of solutions for > 2 and 1 < < 2 in the absence of term Ψ( ) for (14) in [22,23]. However, the influence of non-Newtonian gravitational potential for a practical model was not taken into consideration there.…”

Strong Solutions of Navier-Stokes-Poisson Equations for Compressible Non-Newtonian Fluids

“…In [4], the local existence and uniqueness results of non-Newtonian fluids were given in the case of H norm is small enough. The results on fluid particle interaction non-Newtonian models, see [6][7].…”