Non-uniqueness of Leray-Hopf solutions to the forced fractional Navier-Stokes equations in three dimensions, up to the J. L. Lions exponent

被引：0

作者：

Khor, Calvin ^{[1
]}

Miao, Changxing ^{[2
]}

Su, Xiaoyan ^{[3
,4
]}

机构：

[1] Beijing Computat Sci Res Ctr, Beijing, Peoples R China

[2] Inst Appl Phys & Computat Math, Beijing, Peoples R China

[3] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing, Peoples R China

[4] Beijing Normal Univ, Beijing, Peoples R China

来源：

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | 2023年 / 55卷 / 06期

关键词：

D O I：

10.1112/blms.12889

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show that for & alpha;& ISIN;(1/2,5/4)$\alpha \in (1/2,5/4)$, there exists a force f$f$ and two distinct Leray-Hopf flows u1,u2$u_1,u_2$ solving the forced fractional Navier-Stokes equation starting from rest. This shows that the J. L. Lions exponent is sharp in the class of Leray-Hopf solutions for the forced fractional Navier-Stokes equation.

引用

页码：2705 / 2717

页数：13

共 21 条

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[9] Non-uniqueness of Leray Solutions to the Hypodissipative Navier–Stokes Equations in Two Dimensions
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[10] ON THE RELATION BETWEEN VERY WEAK AND LERAY-HOPF SOLUTIONS TO NAVIER-STOKES EQUATIONS
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