Study On The Well-Posedness Of Solutions For A Class Of Non-Newtonian Micropolar Fluid Equations With Heat Convection

The Navier-Stokes equations for the traditional fluid model are generally stretched out by the idea of micropolar fluid.In generalized continuum mechanics,it is a run-of-the-mill material model.The stable non-Newtonian micropolar fluid equations with heat convection are analyzed in this thesis.Coming up next are the fundamental items:In this thesis we,first and foremost,give a synopsis of the research foundation,brief introduction and the present status of the exploration at home and abroad.In the subsequent part,we present the idea,documentations,certain crucial disparities and primer lemmas of Sobolev spaces.In section three,we concentrate on a class of non-Newtonian micropolar fluid equations with heat convection on accountT₁（D u）=2μ（1+｜Du｜²）^（p-2）/2Duof the pressure tensor.Under the condition that the outside force term and the eddy viscosity coefficient are properly small,we demonstrate the presence and uniqueness of the solid solution of the issue by utilizing the fixed-point theorem to get around the difficulties presented by serious areas of strength for the and solid coupling of the equations.As of section four,we research a class of intensity convection-related non-Newtonian micropolar fluid equations with particular pressure tensors in T₂（D u）=2μ（1+｜Du｜）^（p-2）Du.We initially foster a group of penaltized issues with a boundary to represent the pressure tensor’s absence of consistency,and afterward we utilize the fixed-point theorem to exhibit that these penaltized issues have solid solutions.We exhibit the presence and uniqueness of compelling answers for the issue by embracingε→0.In the last section,we examine the presence and uniqueness of solid solutions for the framework in the situation of two regular pressure tensors.