Energy Equality of Weak Solutions to the Navier-Stokes System in Lorentz Spaces

被引：0
作者：
Wei, Wei [1 ,2 ]
Ye, Yulin [3 ]
机构：
[1] Northwest Univ, Sch Math, Xian 710127, Shaanxi, Peoples R China
[2] Northwest Univ, Ctr Nonlinear Studies, Xian 710127, Shaanxi, Peoples R China
[3] Henan Univ, Sch Math & Stat, Kaifeng 475004, Henan, Peoples R China
来源：
RESULTS IN MATHEMATICS | 2025年 / 80卷 / 03期
基金：
中国国家自然科学基金;
关键词：
Navier-Stokes equations; Euler equations; Energy equality; Lorentz spaces; Littlewood-Paley theory; EQUATIONS;
D O I：
10.1007/s00025-025-02408-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish some novel criteria in terms of the gradient of the velocity in Lorentz spaces for energy equality to both the 3D Navier-Stokes equations and the n-dimensional Euler equations. Our proof mainly relies on Littlewood-Paley theory and Gagliardo-Nirenberg inequalities in Lorentz spaces. To this end, the strong-continuity of translation operators on Lorentz spaces is also proved, which is of independent interest.
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页数：14
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