Energy Conservation of the 4 D Incompressible Navier-Stokes Equations

Q4 Mathematics

应用数学和力学 Pub Date : 2023-01-01 DOI:10.21656/1000-0887.430370

WANG Bin, ZHOU Yanping, BIE Qunyi

引用次数: 0

Abstract

\begin{document}$L^q\left([0, T] ; L^p\left(\mathbb{R}^4\right)\right)$\end{document}

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.

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四维不可压缩Navier-Stokes方程的能量守恒

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 \begin{document}$L^q\left([0, T] ; L^p\left(\mathbb{R}^4\right)\right)$\end{document} 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.

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来源期刊

应用数学和力学 Mathematics-Applied Mathematics

CiteScore

1.20

自引率

0.00%

发文量

6042

期刊介绍： Applied Mathematics and Mechanics was founded in 1980 by CHIEN Wei-zang, a celebrated Chinese scientist in mechanics and mathematics. The current editor in chief is Professor LU Tianjian from Nanjing University of Aeronautics and Astronautics. The Journal was a quarterly in the beginning, a bimonthly the next year, and then a monthly ever since 1985. It carries original research papers on mechanics, mathematical methods in mechanics and interdisciplinary mechanics based on artificial intelligence mathematics. It also strengthens attention to mechanical issues in interdisciplinary fields such as mechanics and information networks, system control, life sciences, ecological sciences, new energy, and new materials, making due contributions to promoting the development of new productive forces.