带有阻尼项的三维Navier-Stokes方程解的收敛性The Convergence of Solutions for the 3D Navier-Stokes Equation with Damping
江洁,张辉
摘要(Abstract)：
带阻尼的Navier-Stokes方程组是描述流体流动规律的一类典型的非线性方程组。从数学结构上来看，当方程组出现阻尼项，其会对解的整体适定性产生调节作用。探讨阻尼项和方程组解之间的各种关系是当前相关领域研究热点。文章探讨了在三维情形下带阻尼项的不可压缩Navier-Stokes方程强解的收敛性问题。通过分析该方程的整体结构和优势，并采用能量估计的方法，描述了当阻尼指标满足2≤β≤4，且阻尼系数α→0时，方程的强解在L~2范数下会一致收敛到Navier-Stokes方程的弱解。
关键词(KeyWords)： Navier-Stokes方程;收敛性;能量估计;阻尼
基金项目(Foundation): 安徽省高等学校优秀青年学者科学基金项目(2023AH030073)
作者(Author): 江洁,张辉
DOI: 10.13757/j.cnki.cn34-1328/n.2025.03.005
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