形变张量的特征值与Boussinesq方程组的正则性估计

王震; 邓大文

doi:10.21656/1000-0887.370355

形变张量的特征值与Boussinesq方程组的正则性估计

doi: 10.21656/1000-0887.370355

王震,
邓大文

湘潭大学数学与计算科学学院, 湖南湘潭 411105

详细信息

作者简介:
王震（1992—），男，硕士生(通讯作者. E-mail: wz05120207@163.com);邓大文（1961—），男，教授，博士，硕士生导师.

中图分类号: O175.29
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- 文章访问数: 1090
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- PDF下载量: 474
- 被引次数: 0
出版历程
- 收稿日期: 2016-11-17
- 修回日期: 2017-01-12
- 刊出日期: 2017-11-15

Eigenvalues of the Deformation Tensor and Regularity Estimates for the Boussinesq Equations

School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P.R.China

摘要

摘要: 讨论了二维及三维满足周期边界条件的Boussinesq方程初边值问题的局部正则解在有限时间内爆破的可能性.在二维情况下，用形变张量的特征值给出温度梯度的L²估计，从中看出若流体微团变形的速率大，则解爆破的可能性就大.在三维情况下，用形变张量的特征值和温度的偏导给出涡量的L²估计，从中发现若流体微团在大部分时间内一般是平面拉伸，且温度的偏导较小时，解爆破的可能性就大；若一般是线性拉伸，温度的偏导又不任意增大时，解爆破的可能性就小.
- Boussinesq方程 /
- 形变张量 /
- 特征值 /
- 正则性估计
Abstract: The blow-up possibility of local regular solutions to the initial-boundary-value problems with periodic boundary conditions for 2D and 3D Boussinesq systems was discussed. In the 2D case, an L² estimate of the temperature gradient was given in terms of the eigenvalues of the deformation tensor. From this estimate it is found that if the deformation rate of a fluid element is large, the regular solution is more likely to blow up. In the 3D case, an L² estimate of the vorticity was given in terms of the eigenvalues of the deformation tensor and the derivatives of temperature. From this estimate it is shown that if for most of the time, most of the fluid elements are stretched in plane and the temperature gradient is small, the regular solution is more likely to blow up. On the contrary, if linear stretching dominates and the temperature gradient is bounded, the solution is less likely to blow up.
- Boussinesq equation /
- deformation tensor /
- eigenvalue /
- regularity estimate

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参考文献(16)

[1]	Chae D, Nam H-S. Local existence and blow-up criterion for the Boussinesq equations[J]. Proceedings of the Royal Society of Edinburgh Section A: Mathematics,1997,127(5): 935-946.
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形变张量的特征值与Boussinesq方程组的正则性估计

doi: 10.21656/1000-0887.370355

作者简介:
王震（1992—），男，硕士生(通讯作者. E-mail: wz05120207@163.com);邓大文（1961—），男，教授，博士，硕士生导师.

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Eigenvalues of the Deformation Tensor and Regularity Estimates for the Boussinesq Equations

计量

目录

留言板

形变张量的特征值与Boussinesq方程组的正则性估计

doi: 10.21656/1000-0887.370355

作者简介: 王震（1992—），男，硕士生(通讯作者. E-mail: wz05120207@163.com);邓大文（1961—），男，教授，博士，硕士生导师.

计量

出版历程

Eigenvalues of the Deformation Tensor and Regularity Estimates for the Boussinesq Equations

计量

出版历程

目录

作者简介:
王震（1992—），男，硕士生(通讯作者. E-mail: wz05120207@163.com);邓大文（1961—），男，教授，博士，硕士生导师.