三维广义Boussinesq方程组的强时间周期解

doi:10.12677/pm.2026.168176

期刊菜单

三维广义Boussinesq方程组的强时间周期解
Strong Time-Periodic Solutions to the Three-Dimensional Generalized Boussinesq Equations

DOI: 10.12677/pm.2026.168176, PDF, 科研立项经费支持
作者: 范风华：华北水利水电大学数学与统计学院，河南郑州；河南省科学院数学研究所，河南郑州；李延硕^*：河南省科学院数学研究所，河南郑州
关键词: 广义Boussinesq方程组；时间周期解；存在性；Generalized Boussinesq System； Time-Periodic Solutions； Existence

摘要: 本文研究了三维光滑有界域上广义Boussinesq方程组的时间周期问题。首先，对原方程组重整化，并引入相应的函数空间。然后，借助算子半群理论、实插值理论和压缩映射原理，证明了定义在单个周期区间上强解的存在唯一性。最后，基于线性重整化系统周期解的存在唯一性和周期延拓，证明了原非线性Boussinesq方程组强时间周期解的存在唯一性。

Abstract: This paper investigates the time-periodic problem for the generalized Boussinesq equations in three-dimensional smooth bounded domains. First, the original system is reformulated and the corresponding function spaces are introduced. Then, by employing operator semigroup theory, real interpolation theory, and the contraction mapping principle, the existence and uniqueness of strong solutions on a single period interval are established. Finally, based on the existence and uniqueness of periodic solutions to the linearized reformulated system and a periodic extension argument, the existence and uniqueness of strong time-periodic solutions to the original nonlinear Boussinesq equations are proved.

文章引用：范风华, 李延硕. 三维广义Boussinesq方程组的强时间周期解[J]. 理论数学, 2026, 16(8): 12-23. https://doi.org/10.12677/pm.2026.168176

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