发表机构
School of Mathematical Sciences, Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University（同济大学数学科学学院，智能计算与应用教育部重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用Green函数方法研究微极方程在Couette流附近的稳定性，提出主导因子提取法处理变系数耦合系统，证明小初始数据下解保持O(μ^{3/4})量级并建立最优衰减估计，为复杂耦合流体系统稳定性分析提供通用框架。
AI 中文摘要
本文利用Green函数方法研究全空间中微极方程解的稳定性。估计Green函数的一个本质困难在于处理具有变系数的耦合方程组，这与先前针对标量方程的Green函数分析完全不同。我们提出了一种主导因子提取方法来克服这一困难。基于微极系统Green函数的精确估计，我们证明：若初始数据(m_0, \omega_0)满足\\|(m_0, \omega_{0})\\|_{L^1\cap L^{\infty}}\leq c_0\mu^{3/4}，其中c_0为不依赖于粘性系数\mu的小常数，则在Couette流作用下，相应解保持O(\mu^{3/4})量级。同时，我们建立了解在一般L^p范数下的最优衰减估计。更重要的是，本文发展的主导因子提取方法为复杂耦合流体系统的稳定性分析提供了一个通用框架。
英文摘要
In this paper, we use the Green's function method to study the stability of solutions to micropolar equations in the whole space. An essential difficulty in estimating the Green's function lies in treating a coupled system of equations with variable coefficients, which is completely different from previous Green's function analyses for scalar equations. We propose a dominant factor extraction method to overcome this difficulty. Based on sharp Green's function estimates for the micropolar system, we prove that if the initial data (m_0, ω_0) satisfy \|(m_0, ω_{0})\|_{L^1\cap L^{\infty}}\leq c_0μ^{3/4} for some small constant c_0 independent of the viscosity coefficient μ, then the corresponding solution remains of order O(μ^{3/4}) under the effect of the Couette flow. Meanwhile, we establish the optimal decay estimates of solutions in the general L^p norm. More importantly, the dominant factor extraction method developed in this work provides a general framework for the stability analysis of complex coupled fluid systems.
Comments23 pages, no figures
