四维不可压缩Navier-Stokes方程的能量守恒

王斌; 周艳平; 别群益

doi:10.21656/1000-0887.430370

四维不可压缩Navier-Stokes方程的能量守恒

doi: 10.21656/1000-0887.430370

三峡大学理学院，湖北宜昌 443002

基金项目:

国家自然科学基金项目 11901346

国家自然科学基金项目 11871305

详细信息

作者简介:
王斌(1998—)，女，硕士生(E-mail: 2895969956@qq.com)

别群益(1970—)，男，教授，博士，博士生导师(E-mail: qybie@126.com)

通讯作者:
周艳平(1980—)，女，副教授，博士(通讯作者. E-mail: zhyp5208@163.com)

中图分类号: O175.2
计量
- 文章访问数: 214
- HTML全文浏览量: 72
- PDF下载量: 61
- 被引次数: 0
出版历程
- 收稿日期: 2022-11-16
- 修回日期: 2022-12-24
- 刊出日期: 2023-08-01

Energy Conservation of the 4 D Incompressible Navier-Stokes Equations

College of Science, China Three Gorges University, Yichang, Hubei 443002, P.R.China

摘要

摘要: 研究了四维不可压缩Navier-Stokes方程的能量守恒，当该方程的Leray-Hopf弱解(适当弱解)存在维数小于4的奇异集时，基于Wu在文章中关于四维不可压缩Navier-Stokes方程的部分正则性结果，得到了四维空间中$L^q\left([0, T] ; L^p\left(\mathbb{R}^4\right)\right)$条件，保证该方程能量守恒.
- Navier-Stokes方程 /
- 部分正则性 /
- 能量守恒
Abstract: The energy conservation of 4D incompressible Navier-Stokes equations was studied. In the case of a singular set with a dimension number less than 4 for the Leray-Hopf weak solution (suitable weak solution), the $L^q\left([0, T] ; L^p\left(\mathbb{R}^4\right)\right)$ condition in the 4D space was obtained based on Wu's partial regularity results about the 4D incompressible Navier-Stokes equations, to ensure the energy conservation.
- Navier-Stokes equation /
- partial regularity /
- energy conservation

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图 1 d=0

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图 2 0 < d < 2

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图 3 d=2

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图 4 2 < d < 4

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