ON THE ENERGY EQUALITY FOR WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS
In this paper, we first introduce the concept of absolutely continuous functions of order s(0 < s ≤ 1). Next, we prove the energy equality for weak solutions of the Navier-Stokes equations (NSE) in bounded three dimensional domains if and only if u is an absolutely continuous solution of order 1/2. Finally, we present a sufficient condition for the energy equality of weak solutions to NSE. Here, we prove that if then the energy equality holds.
Navier-Stokes equations, energy equality, energy inequality, weak solution.
Received: October 11, 2022; Accepted: November 15, 2022; Published: December 12, 2022
How to cite this article: N. V. Giang, D. Q. Khai and N. M. Tri, On the energy equality for weak solutions of the Navier-Stokes equations, Advances in Differential Equations and Control Processes 29 (2022), 101-115. http://dx.doi.org/10.17654/0974324322035
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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