Energy Conservation of the 4 D Incompressible Navier-Stokes Equations

WANG Bin; ZHOU Yanping; BIE Qunyi

doi:10.21656/1000-0887.430370

Volume 44 Issue 8

Aug. 2023

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WANG Bin, ZHOU Yanping, BIE Qunyi. Energy Conservation of the 4 D Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2023, 44(8): 999-1006. doi: 10.21656/1000-0887.430370

Citation:

WANG Bin, ZHOU Yanping, BIE Qunyi. Energy Conservation of the 4 D Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2023, 44(8): 999-1006. doi: 10.21656/1000-0887.430370

Citation:

WANG Bin, ZHOU Yanping, BIE Qunyi. Energy Conservation of the 4 D Incompressible Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2023, 44(8): 999-1006. doi: 10.21656/1000-0887.430370

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Energy Conservation of the 4 D Incompressible Navier-Stokes Equations

doi: 10.21656/1000-0887.430370

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

Received Date: 2022-11-16
Rev Recd Date: 2022-12-24
Publish Date: 2023-08-01

Abstract

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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References(26)

References

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