| This thesis mainly investigates the large-time behavior of solution to one-dimensional compressible p-th micropolar fluid with viscous and thermal conductivity.The model is used to study the microscopic phenomena of materials with microstructure.The model includes not only the case of p =1,but also the case of p(29)1.Under some conditions,the fluid model can more accurately describe fluid motion than the ideal gas model(p =1).This thesis is separated into four chapters.In chapter 1,we briefly discuss the research background and current status of compressible p-th micropolar fluid equations,and provide some commonly used inequalities.In chapter 2,we investigate the large time behavior of the solution of the one-dimensional compressible p-th micropolar fluid model when both the viscosity coefficient and the thermal conductivity coefficient are constant,the velocity and the micro rotational velocity satisfy the Dirichlet boundary condition,and the absolute temperature function satisfies the Neumann boundary condition.Based on the existence of the local solution constructed by Ba(?)i(?)-(?)i(?)ko and Dra(?) i(?),we prove the uniform upper and lower bounds of the density function and the temperature function by using energy estimation method,and acquire the existence of the global solution.These prior estimates are independent of the time.Then,we analyze the asymptotic behavior of the solution when the time inclines to infinity,and further prove that the solution is exponentially stable.At the end of chapter 2,we briefly analyze the asymptotic behavior and regularity of the solution of the model in unbounded domain with fixed end and far field boundary conditions at the other end.In chapter 3,if the viscosity coefficient and thermal conductivity coefficient are not constant,we consider the global existence of the solution for the model under the stress-free boundary conditions when the viscosity coefficient is the power of the density function and the thermal conductivity coefficient is the power of the temperature function.The fourth chapter summarizes the research results of this thesis and puts forward several problems that we will study in the future. |
