Dynamics Of Three-Dimensional Fully Compressible Micropolar Fluid Equations With Vacuum At Infinity

The micropolar fluid equation is the fundamental partial differential equa-tion in micropolar fluid mechanics,which is a complex fluid with a microstruc-ture consisting of suspended particles and a viscous base fluid.The micropolar fluid equation describes the laws of motion of animal blood,liquid crystals,di-lute aqueous polymer solutions,etc.and is widely used in branches of physics as well as in theoretical studies of engineering and technology.This paper studies the fitness and long-time behaviour of solutions of the Cauchy problem for fully compressible micropolar fluids in~3.Based on the current state of research on the overall existence of solutions in the isentropic and non-isentropic cases and on the overall dynamics of the internal region-al vacuum and large oscillations,we apply fine energy estimates,initial layer analysis,continuation theory,the type of the solution region(periodic domain or full space)and other factors to establish valid a priori estimates of the solu-tions of the equations for fully compressible micropolar fluids,and then,with the help of continuum methods and local existence theory,to establish the strong solution The study is then extended from the internal region vacuum case to the vacuum case with infinite fields.On the long-time behaviour of the equations for full compressible microp-olar fluids.The long-time behaviour of the solution is established based on the results of previous work on decay estimates for solutions of the Cauchy prob-lem for three-dimensional isentropic incompressible micropolar fluids obtained in the framework of small perturbations,and their results are extended from the incompressible case to the fully compressible case,and decay estimates for the solution are established.The next research direction is then planned to extend the consideration of viscosity coefficients dependent on density,full space regions to problems in bounded or outer regions.On the other hand,we also study the global well-posedness and long time behavior of the magnetic micropolar fluid equations.