带状域无浮力扩散的二维Boussinesq方程的稳定性
Stability of the 2D Boussinesq Equations without Buoyancy Diffusion in Strip Domain
DOI: 10.12677/AAM.2023.124174, PDF,   
作者: 成子强, 任晓霞*：华北电力大学数理学院，北京
关键词: Boussinesq方程；带状域；低正则性 ；Boussinesq Equations； Strip Domain； Low Regularity
摘要: 我们证明了带状域R×(0,1)中不含浮力扩散具有Navier型滑移边界条件的二维Boussinesq方程在平衡状态(0,x2)附近的全局适定性。值得一提的是，本文仅利用能量估计，方程自身结构以及∂1u利普希茨范数的衰减率即可获得低正则性结果。
Abstract: We prove the global well-posedness for the 2D Boussinesq equations without buoyancy diffusion around the equilibrium state (0,x2) in the strip domain R×(0,1) with Navier-type slip boundary condition. It is worth mentioning that the results of low regularity are obtained using only the en-ergy estimate, the structure of the equations and the decay rate of Lip norm of ∂1u .
文章引用：成子强, 任晓霞. 带状域无浮力扩散的二维Boussinesq方程的稳定性[J]. 应用数学进展, 2023, 12(4): 1683-1689. https://doi.org/10.12677/AAM.2023.124174

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