Remarks on the weak formulation of the Navier-Stokes equations on the 2D hyperbolic space

Chi-Hin Chan; Magdalena Czubak

doi:10.1016/j.anihpc.2015.01.002

Remarks on the weak formulation of the Navier-Stokes equations on the 2D hyperbolic space

Chi-Hin Chan, Magdalena Czubak^*

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

The Leray-Hopf solutions to the Navier-Stokes equation are known to be unique on R². In our previous work, we showed the breakdown of uniqueness in a hyperbolic setting. In this article, we show how to formulate the problem in order so the uniqueness can be restored.

Original language	English
Pages (from-to)	655-698
Number of pages	44
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	33
Issue number	3
DOIs	https://doi.org/10.1016/j.anihpc.2015.01.002
State	Published - 1 May 2016

Keywords

Harmonic forms
Hyperbolic space
Leray-Hopf
Navier-Stokes
Non-uniqueness
Uniqueness

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10.1016/j.anihpc.2015.01.002

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abstract = "The Leray-Hopf solutions to the Navier-Stokes equation are known to be unique on R2. In our previous work, we showed the breakdown of uniqueness in a hyperbolic setting. In this article, we show how to formulate the problem in order so the uniqueness can be restored.",

keywords = "Harmonic forms, Hyperbolic space, Leray-Hopf, Navier-Stokes, Non-uniqueness, Uniqueness",

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KW - Non-uniqueness

KW - Uniqueness

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Remarks on the weak formulation of the Navier-Stokes equations on the 2D hyperbolic space

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Keywords

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