一维可压缩微极流模型解的衰减率  

Decay Rates of Solutions for the One-dimensional Compressible Micropolar Fluid Model

作　　者：王迪 WANG DI(Department of Eletronic and Information Engineering,Bozhou Uiversity,Bozhou 236800,China)

机构地区：[1]亳州学院电子与信息工程系,亳州236800

出　　处：《应用数学学报》2025年第1期117-138,共22页Acta Mathematicae Applicatae Sinica

基　　金：安徽省高等学校科学研究项目(No.2024AH051311)资助。

摘　　要：本文主要研究粘性系数依赖于密度的一维等熵可压缩微极流模型解的时间衰减率问题.对于参数α,γ∈R,考虑压强p(ρ)=ρ^(γ)和粘性系数μ(ρ)=ρ^(α).我们首先利用先验假设及一些精细的能量估计,研究一维等熵可压缩微极流模型Cauchy问题在常数状态扰动下大初值强解的整体存在性与大时间行为.进一步,利用反导数和时间加权能量方法,我们研究流体比容v(t,x)和速度u(t,x)的时间衰减率.This paper is concerned with the time decay rates of strong solutions for the one-dimensional isentropic compressible micropolar fluid model with density-dependent viscosity.The pressure p(p)=ρ^(α) and the viscosity coeficient μ(p)=ρ^(α) for some parameters α,γ∈R are considered.By using a priori assumption and some refined energy estimates,we show that the global existence and large-time behavior of strong solutions with large initial data for the Cauchy problem under the perturbation of the constant state.Furthermore,by using the anti-derivative and time weighted energy method,the algebraic time decay rates for the specific volume v(t,x)and the velocity u(t,x)are also established.

关 键 词：微极流方程 整体稳定性 衰减率 

分 类 号：O175.29[理学—数学]