The 3D incompressible Boussinesq equations with fractional partial dissipation
The 3D incompressible Boussinesq equations with fractional partial dissipation
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DOI：
10.4310/cms.2018.v16.n3.a2
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发表时间：
2018
影响因子：
1
通讯作者：
Wanrong Yang;Q. Jiu;Jiahong Wu
中科院分区：
文献类型：
--
作者：
Wanrong Yang;Q. Jiu;Jiahong Wu
三维Boussinesq方程组是地球物理流体最重要的模型之一。具有标准Laplacian耗散的三维Boussinesq方程的合理光滑解是否能在有限时间内爆破的基本问题是一个悬而未决的公开问题。具有部分或分数阶耗散的Boussinesq方程不仅是经典Boussinesq方程的自然推广，而且在物理意义和数学意义上都很重要。本文研究了一类具有分数阶部分耗散的三维Boussinesq方程组，证明了任何H1初值都能得到唯一的整体时间解.本文的结果是我们致力于最小耗散Boussinesq方程的整体适定性问题的努力的一部分。
The system of the 3D Boussinesq equations is one of the most important models for geophysical fluids. The fundamental problem of whether or not reasonably smooth solutions to the 3D Boussinesq equations with the standard Laplacian dissipation can blow up in a finite time is an outstanding open problem. The Boussinesq equations with partial or fractional dissipation not only naturally generalize the classical Boussinesq equations, but also are physically relevant and mathematically important. This paper focuses on a system of the 3D Boussinesq equations with fractional partial dissipation and proves that any H1-initial data always leads to a unique and global-in-time solution. The result of this paper is part of our efforts devoted to the global well-posedness problem on the Boussinesq equations with minimal dissipation.