| This paper primarily studies the compressible micropolar fluid system,which is a generalization of classical Navier-Stokes system,has a wide range of applications in many fields,for example,the construction of water conservancy projects,the design of aircraft,the air flow around the wings of the aircraft,the flow of liquids in the pipes,etc...On the basis of the paper[18],studies the decay rate of higher-order derivatives of the solution to the Cauchy problem on the compressible micropolar fluid system in R3.To be more precise,when the initial value is sufficiently close to the steady-state solution[p=1,u=0,ω=0],it turns out that both the density and the velocity tend time-asymptotically to the corresponding equilibrium state with rate(1+t)-3/4 in L2 norm and the micro-rotational velocity also tends to the equilibrium state with the faster rate(1+t)-5/4 in L2 norm.Based on the results of liu and zhang,inspired by literature[13,24],by applying the energy estimate method and the Fourier splitting method to turn out the first order spatial derivative decay estimate of solution in H3 norm is(1+t)-5/4and the second spatial derivative decay estimate of the solution in H2 norm is(1+t)-7/4.This paper is divided into four chapters:The first chapter,which summarizes the background,significance of the research and research progress.Briefly describes the main work of this study and the difficulties encountered in the process of proof.The second chapter,briefly introduced some important inequalities used in the pro-cess of proof in this article,some special symbols,marks and the perturbation equations of the original model about the constant state.The third chapter,gives the decay rate of first order derivatives of the solution to the Cauchy problem on the compressible micropolar fluid system.The fourth chapter,gives the decay rate of second order derivatives of the solution to the Cauchy problem on the compressible micropolar fluid system. |
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