Euler and Navier-Stokes equations on the hyperbolic plane

被引：18

作者：

Khesin, Boris ^{[1
,2
]}

Misiolek, Gerard ^{[1
,3
]}

机构：

[1] Inst Adv Study, Sch Math, Princeton, NJ 08450 USA

[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

[3] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

来源：

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA | 2012年 / 109卷 / 45期

基金：

加拿大自然科学与工程研究理事会;

关键词：

harmonic forms; steady flows; ill-posedness; Dirichlet problem; Dodziuk's theorem; DIRICHLET PROBLEM; INFINITY;

D O I：

10.1073/pnas.1210350109

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We show that nonuniqueness of the Leray-Hopf solutions of the Navier-Stokes equation on the hyperbolic plane H-2 observed by Chan and Czubak is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on H-n whenever n >= 3. We also describe the corresponding general Hamiltonian framework of hydrodynamics on complete Riemannian manifolds, which includes the hyperbolic setting.

引用

页码：18324 / 18326

页数：3

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