Finite-time singularity formation for C1,α solutions to the incompressible Euler equations on R3

被引：89
作者：
Elgindi, Tarek M. [1 ,2 ]
机构：
[1] Univ Calif San Diego, La Jolla, CA 92093 USA
[2] Duke Univ, Durham, NC 27708 USA
来源：
ANNALS OF MATHEMATICS | 2021年 / 194卷 / 03期
关键词：
Euler equations; singularity formation; asymptotic stability; NAVIER-STOKES EQUATIONS; SELF-SIMILAR SOLUTIONS; VORTICITY GRADIENT; BLOW-UP; EXPONENTIAL-GROWTH; ENERGY; FLOWS;
D O I：
10.4007/annals.2021.194.3.2
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It has been known since work of Lichtenstein and Gunther in the 1920s that the 3D incompressible Euler equation is locally well-posed in the class of velocity fields with Ho center dot lder continuous gradient and suitable decay at infinity. It is shown here that these local solutions can develop singularities in finite time, even for some of the simplest three-dimensional flows.
引用
收藏
页码：647 / 727
页数：82
相关论文
共 60 条
[1]   On the global well-posedness for the axisymmetric Euler equations [J].
Abidi, Hammadi ;
Hmidi, Taoufik ;
Keraani, Sahbi .
MATHEMATISCHE ANNALEN, 2010, 347 (01) :15-41
[2]  
Bardos C, 2007, RUSS MATH SURV+, V62, P409, DOI [10.1070/RM2007v062n03ABEH004410, 10.4213/rm6811]
[3]   REMARKS ON THE BREAKDOWN OF SMOOTH SOLUTIONS FOR THE 3-D EULER EQUATIONS [J].
BEALE, JT ;
KATO, T ;
MAJDA, A .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1984, 94 (01) :61-66
[4]   Convex integration and phenomenologies in turbulence [J].
Buckmaster, Tristan ;
Vicol, Vlad .
EMS SURVEYS IN MATHEMATICAL SCIENCES, 2019, 6 (1-2) :173-263
[5]   Nonexistence of self-similar singularities for the 3D incompressible Euler equations [J].
Chae, Dongho .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 273 (01) :203-215
[6]   On Formation of a Locally Self-Similar Collapse in the Incompressible Euler Equations [J].
Chae, Dongho ;
Shvydkoy, Roman .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2013, 209 (03) :999-1017
[7]   On the Finite-Time Blowup of a One-Dimensional Model for the Three-Dimensional Axisymmetric Euler Equations [J].
Choi, Kyudong ;
Hou, Thomas Y. ;
Kiselev, Alexander ;
Luo, Guo ;
Sverak, Vladimir ;
Yao, Yao .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2017, 70 (11) :2218-2243
[8]   A SIMPLE ONE-DIMENSIONAL MODEL FOR THE 3-DIMENSIONAL VORTICITY EQUATION [J].
CONSTANTIN, P ;
LAX, PD ;
MAJDA, A .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (06) :715-724
[9]  
Constantin P, 2000, INT MATH RES NOTICES, V2000, P455
[10]  
Constantin P, 1996, COMMUN PART DIFF EQ, V21, P559
123456