Well-posedness Of Two Classes Of Non-newtonian Flow Equations With Particle Interaction

The fluid-particle interaction model has been widely used in many practical applications and plays an important role in the analysis of the sedimentation of dispersed suspended particles in fluids.At present,one of the commonly used models in the fields of biotechnology,medicine,mineral processing and chemical industry.In daily life and many physical processes,non-Newtonian fluids can be seen everywhere.Therefore,it is very important to study the properties of compressible non-Newtonian fluids with particle interaction.Classical Newtonian fluid mechanics considers that when the stress and strain rates are linear,the fluid is called Newtonian fluid.The coefficient of proportion is called the coefficient of viscosity.If the relationship is not linear,the fluid is called a non-Newtonian fluid.In order to deepen the understanding of the properties of non-Newtonian fluids with particle interaction,two kinds of non-Newtonian physical equations with particle interaction are studied,and the well-possibility of their strong solutions is discussed.The contents are as follows:The well-posedness of a class of compressible non-Newtonian fluids with gravitational potential and particle interaction is studied.Under the initial condition of vacuum and no external force,there exists a time that satisfies the initial boundary value condition of the equation,so that there exists a unique local strong solution of the equation.Because the system of equations has singularity,by introducing a regularization process to overcome this difficulty,and then back to the original problem will limit process,set up the auxiliary function,according to estimates of the auxiliary function,essentially it are obtained,overcome the singularity of the equations and the strong coupling,and prove that such well-posedness of compressible non-Newtonian fluid equations.The fitness of a compressible non-Newtonian fluid with viscosity dependent density and particle interaction is studied,When the initial conditions are vacuum and the viscosity dependent density is present,there exists a time that satisfies the initial boundary condition of the equation,so that the system has a unique local strong solution.Since the equations have strong nonlinear and coupling properties,according to conservation of mass and conservation of momentum,get consensus estimates,overcome the influence of coupling equations,ultimately proved such well-posedness of compressible non Newtonian fluid.