Global Well-posedness Of Solution To Compressible Micropolar Fluid

This thesis mainly studies the global well-posedness of solution to three-dimensional spherically symmetric and cylindrically symmetric compressible viscous micropolar fluid.Compared with the classical Navier-Stokes equations,there is an additional angular velocity term in the micropolar fluid equations.The damping term of the angular velocity contained in the equation provides better regularity for the study,but it also increases the nonlinearity of the system.This thesis is unfolded as four chapters.The first chapter introduces the background and research status of the compressible micropolar fluid equations.The second chapter is concerned with the global well-posedness of the solution of the three-dimensional cylindrically symmetric compressible viscous micropolar fluid inH~2.Under the condition that the initial energy is very small,we use the method of energy estimate,embedding theorems,interpolation inequalities and other techniques to prove the global well-posedness of the solution.The third chapter improves the regularity of the initial value on the basis of the second chapter,and proves the regularity of the solution of the three-dimensional cylindrically symmetric compressible viscous micropolar fluid inH~4.The fourth chapter dicusses the large-time behavior of the solution to the spherically symmetric compressible viscous micropolar fluid equations.At present,there have been many results in bounded annular domains in R~3.This paper is concerned with the large-time behavior of solution to the initial boundary value problems with large initial data for the compressible micropolar fluid in unbounded domain exterior to a ball in R~3.Based on the method of energy estimate,we prove that the temperature has uniform upper and lower bounds,and when the time tends to infinity,the global solution is asymptotically stable.