时间加权的Besov空间上带外力的分数阶Navier-Stokes方程OA
Fractional Navier-Stokes equations with external forces in time-weighted Besov spaces
讨论分数阶Navier-Stokes方程在时间加权的Besov空间中mild解的存在性和唯一性.基于Lebesgue控制收敛定理、Banach空间隐函数定理、Besov空间上Navier-Stokes方程的Lp-Lq估计以及 Mittag-Leffler函数的相关性质,给出了具有小初始数据和外力的情况下该方程全局mild解的存在性和唯一性定理,并研究了给定数据下局部mild解的存在性.
This paper discusses the existence and uniqueness of mild solutions of fractional Navier-Stokes equations in time-weighted Besov spaces.The existence and uniqueness theorems of global mild solutions with small initial data and external forces are given,and the existence results of local mild solutions with given data are studied.The proofs are mainly based on the Lebesgue convergence theorem,implicit function theorem of Banach space,Lp-Lq estimation of Navier-Stokes equations in Besov spaces and relative properties of Mittag-Leffler functions.
李琳玉;杨和
西北师范大学 数学与统计学院,甘肃 兰州 730070西北师范大学 数学与统计学院,甘肃 兰州 730070
数理科学
分数阶Navier-Stokes方程时间加权的Besov空间mild解适定性
fractional Navier-Stokes equationtime-weighted Besov spacemild solutionwell-posedness
《西北师范大学学报（自然科学版）》 2026 (1)
77-92,16
国家自然科学基金资助项目(12461037)甘肃省自然科学基金资助项目(24JRRA780)
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