ON THE ENERGY EQUALITY FOR WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS

被引：0

作者：

Giang, N., V ^{[1
]}

Khai, D. Q. ^{[2
]}

Tri, N. M. ^{[2
]}

机构：

[1] Thai Nguyen Univ Technol, Fac Basic Sci, 666,3-2 St, Tich Luong, Thai Nguyen, Vietnam

[2] Vietnam Acad Sci & Technol, Inst Math, 18 Hoang Quoc Viet, Hanoi 10307, Vietnam

来源：

ADVANCES IN DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES | 2022年 / 29卷

关键词：

Navier-Stokes equations; energy equality; energy inequality; weak solution;

D O I：

10.17654/0974324322035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 u is an element of L-2 (0,T,H-s) boolean AND L-4 (0, T; L (12/2s+1) ) ( <= s < 5/2), then the energy equality holds.

引用

页码：101 / 115

页数：15

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