发表机构
CRAN-UMR-CNRS-7039 University of Lorraine（洛林大学 CRAN-UMR-CNRS-7039）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对三维不可压缩纳维-斯托克斯方程，引入局域 coercivity 性质，在非自治框架下建立指数能量衰减，并提出有限维谱量作为 coercivity 的可计算代理，为降阶模型给出显式衰减估计。
AI 中文摘要
本文针对带有空间局域耗散的三维不可压缩纳维-斯托克斯方程，在动能与Leray-Hopf弱解层面开展基于能量的分析。引入了将粘性与阻尼关联到全局L²控制的局域 coercivity 性质，并将其与关联斯托克斯算子的可观测性和谱不等式相联系。在该条件下，无需正则性或线性化假设即可建立指数能量衰减，且在非自治框架下处理了随时间变化的阻尼。提出了一种有限维谱量作为 coercivity 的可计算代理，为降阶模型给出了显式衰减估计。
英文摘要
Energy-based analysis of the three-dimensional incompressible Navier--Stokes equations with spatially localized dissipation is developed at the level of kinetic energy and Leray--Hopf weak solutions. A localized coercivity property linking viscosity and damping to global $L^2$ control is introduced and related to observability and spectral inequalities for the associated Stokes operator. Under this condition, exponential energy decay is established without regularity or linearization assumptions, and time-dependent damping is treated within a nonautonomous framework. A finite-dimensional spectral quantity is proposed as a computable proxy for coercivity, yielding explicit decay estimates for reduced-order models.
Comments27 pages
