Nonuniqueness of solutions of the Navier-Stokes equations on Riemannian manifolds

被引：15

作者：

Lichtenfelz, Leandro A. ^{[1
]}

机构：

[1] Univ Notre Dame, Dept Math, South Bend, IN 46556 USA

来源：

ANNALS OF GLOBAL ANALYSIS AND GEOMETRY | 2016年 / 50卷 / 03期

关键词：

Navier-Stokes; Harmonic vector fields; Ill-posedness; MOTION;

D O I：

10.1007/s10455-016-9509-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct nonunique solutions of Leray-Hopf type of the Navier-Stokes equations on a noncompact three-dimensional manifold of negative curvature. This answers a question raised by C. Chan and M. Czubak.

引用

页码：237 / 248

页数：12

共 50 条

[41] ON APPROXIMATE INERTIAL MANIFOLDS FOR STOCHASTIC NAVIER-STOKES EQUATIONS
CHUESHOV, ID
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 196 (01) : 221 - 236
[42] Sharp nonuniqueness for the Navier–Stokes equations
Alexey Cheskidov
Xiaoyutao Luo
Inventiones mathematicae, 2022, 229 : 987 - 1054
[43] The convergence of the solutions of the Navier-Stokes equations to that of the Euler equations
Temam, R
Wang, X
APPLIED MATHEMATICS LETTERS, 1997, 10 (05) : 29 - 33
[44] On the regularity of the axisymmetric solutions of the Navier-Stokes equations
Chae, D
Lee, J
MATHEMATISCHE ZEITSCHRIFT, 2002, 239 (04) : 645 - 671
[45] Uniqueness of weak solutions of the Navier-Stokes equations
Sadek Gala
Applications of Mathematics, 2008, 53 : 561 - 582
[46] Pump flow solutions of the Navier-Stokes equations
Öztekin, A
Seymour, BR
Varley, E
STUDIES IN APPLIED MATHEMATICS, 2001, 107 (01) : 1 - 41
[47] SMOOTHNESS OF WEAK SOLUTIONS OF NAVIER-STOKES EQUATIONS
KANIEL, S
SHINBROT, M
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1967, 24 (04) : 302 - &
[48] EXACT DALEMBERT SOLUTIONS OF NAVIER-STOKES EQUATIONS
THOMAS, JP
PASSMAN, SL
SIAM REVIEW, 1978, 20 (03) : 635 - 635
[49] SOLUTIONS OF THE NAVIER-STOKES EQUATIONS IN IMPLICIT FORM
RANGER, KB
QUARTERLY OF APPLIED MATHEMATICS, 1992, 50 (04) : 793 - 800
[50] LENGTH SCALES IN SOLUTIONS OF THE NAVIER-STOKES EQUATIONS
BARTUCCELLI, MV
DOERING, CR
GIBBON, JD
MALHAM, SJA
NONLINEARITY, 1993, 6 (04) : 549 - 568

← 1 2 3 4 5 →