Existence Of Global Solutions For Fluid Equations

In this paper,we mainly study the global strong solutions for 3D viscous incompressible heat conducting N-S flows with the general external force,and the global strong solutions and classical solutions of the 3D nonhomogeneous incompressible magneto-micropolar fluids.The full paper is divided into the following three parts:In the first part,we first introduce the N-S equations and magneto-micropolar fluid equations,and then we present the research background and status of the N-S equations and the magneto-micropolar fluids.In the second part,we study the initial boundary value problem for the nonhomogeneous heat conducting N-S flows with vacuum and the general force,we mainly prove that there exists a global strong solution to the 3D viscous incompressible heat conducting N-S flows if(?)is suitably small.In the third part,we study the global well-posedness of strong and classical solutions for the 3D inhomogeneous incompressible magneto-micropolar fluids with vacuum.Under proper conditions,we first prove that there exists a global strong solution for 3D nonhomogeneous incompressible magneto-micropolar fluids.Next,combining with compatibility conditions and improving the regularity of the initial value,we get the classical solutions.