一类不可压非牛顿Boussinesq方程组正则解的存在性
Existence of Regular Solution for a Class of Incompressible Non-Newton Boussinesq Equations
DOI: 10.12677/AAM.2023.124192, PDF,  被引量    科研立项经费支持
作者: 刘 琳*, 王长佳：长春理工大学数学与统计学院，吉林 长春
关键词: 非牛顿流；Boussinesq方程组；奇异性；正则性；Non-Newtonian Flow； Boussinesq Equation； Singularity； Regular Solution
摘要: 在三维光滑有界区域中研究了奇异情况下的非牛顿Boussinesq方程组的周期初边值问题。应用Galerkin方法、Gronwall不等式、Aubin-Lions引理，并结合能量估计、紧性方法证明了外力项适当小的情况下，该方程组正则解的存在性。
Abstract: The periodic initial boundary value problem of non-Newtonian Boussinesq equations in singular case is studied in three-dimensional smooth bounded domain. By using Galerkin method, Gronwall inequality, Aubin-Lions lemma, energy estimation and compactness method, the existence of regu-lar solutions for the system is proved when the external force term is appropriately small.
文章引用：刘琳, 王长佳. 一类不可压非牛顿Boussinesq方程组正则解的存在性[J]. 应用数学进展, 2023, 12(4): 1855-1865. https://doi.org/10.12677/AAM.2023.124192

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