Affiliation:
1. College of Mathematics and Information Science Zhengzhou University of Light Industry Zhengzhou P.R. China
2. School of Mathematics and Statistics Henan University Kaifeng P.R. China
Abstract
In this paper, we derive an energy conservation criterion based on a combination of velocity and its gradient for the weak solutions of both the homogeneous incompressible Navier–Stokes equations and the general compressible Navier–Stokes equations. For the incompressible case, this class implies almost known corresponding results on periodic domain via either the velocity or its gradient including the famous Lions' energy conservation criterion obtained in [1, Rend. Semin. Mat. Univ. Padova, 30 (1960)]. For the compressible case, this helps us to extend the previously known criteria for the energy conservation of weak solutions from the incompressible fluid to compressible flow and improve the recent results due to Nguyen‐Nguyen‐Tang in [26, Nonlinearity, 32 (2019)] and Liang in [27, Proc. Roy. Soc. Edinburgh Sect. A, (2020)].
Funder
China Postdoctoral Science Foundation
National Natural Science Foundation of China
Subject
General Engineering,General Mathematics
Reference35 articles.
1. Sur la régularité et l'unicité des solutions turbulentes des équations de Navier Stokes;Lions JL;Rend Semin Mat Univ Padova,1960
2. Un teorema di unicità per le equazioni di Navier-Stokes
3. SerrinJ.The initial value problem for the Navier‐Stokes equations. In: Nonlinear Problems Proc Sympos Madison;1963:69‐98.
4. The Energy Equation for the Navier–Stokes System
5. On the Shinbrot's criteria for energy equality to Newtonian fluids: a simplified proof, and an extension of the range of application;Beirao da Veiga H;Nonlinear Anal,2020
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献