Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. III. Two singularities

Li Li; Yanyan Li; Xukai Yan

doi:10.3934/dcds.2019300

Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. III. Two singularities

Li Li, Yanyan Li, Xukai Yan

SAS - Mathematics

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

Abstract

All (−1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus north and south poles have been classified in our earlier work as a four dimensional surface with boundary. In this paper, we establish near the no-swirl solution surface existence, non-existence and uniqueness results on (−1)-homogeneous axisymmetric solutions with nonzero swirl which are smooth on the unit sphere minus north and south poles.

Original language	English (US)
Pages (from-to)	7163-7211
Number of pages	49
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	39
Issue number	12
DOIs	https://doi.org/10.3934/dcds.2019300
State	Published - 2019

All Science Journal Classification (ASJC) codes

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Keywords

Existence
Homogeneous solutions
Isolated singularities
Stationary Navier-Stokes equations
Uniqueness

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title = "Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. III. Two singularities",

abstract = "All (−1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus north and south poles have been classified in our earlier work as a four dimensional surface with boundary. In this paper, we establish near the no-swirl solution surface existence, non-existence and uniqueness results on (−1)-homogeneous axisymmetric solutions with nonzero swirl which are smooth on the unit sphere minus north and south poles.",

keywords = "Existence, Homogeneous solutions, Isolated singularities, Stationary Navier-Stokes equations, Uniqueness",

author = "Li Li and Yanyan Li and Xukai Yan",

note = "Funding Information: 2010 Mathematics Subject Classification. Primary: 35Q30, 76D03; Secondary: 76D05. Key words and phrases. Homogeneous solutions, stationary Navier-Stokes equations, isolated singularities, existence, uniqueness. The first named author is partially supported by NSFC grants 11871177. The second named author is partially supported by NSF grants DMS-1501004. The third named author is partially supported by AMS-Simons Travel Grant and AWM-NSF Travel Grant 1642548. ∗ Corresponding author: Xukai Yan.",

year = "2019",

doi = "10.3934/dcds.2019300",

language = "English (US)",

volume = "39",

pages = "7163--7211",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "12",

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TY - JOUR

T1 - Homogeneous solutions of stationary Navier-Stokes equations with isolated singularities on the unit sphere. III. Two singularities

AU - Li, Li

AU - Li, Yanyan

AU - Yan, Xukai

N1 - Funding Information: 2010 Mathematics Subject Classification. Primary: 35Q30, 76D03; Secondary: 76D05. Key words and phrases. Homogeneous solutions, stationary Navier-Stokes equations, isolated singularities, existence, uniqueness. The first named author is partially supported by NSFC grants 11871177. The second named author is partially supported by NSF grants DMS-1501004. The third named author is partially supported by AMS-Simons Travel Grant and AWM-NSF Travel Grant 1642548. ∗ Corresponding author: Xukai Yan.

PY - 2019

Y1 - 2019

N2 - All (−1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus north and south poles have been classified in our earlier work as a four dimensional surface with boundary. In this paper, we establish near the no-swirl solution surface existence, non-existence and uniqueness results on (−1)-homogeneous axisymmetric solutions with nonzero swirl which are smooth on the unit sphere minus north and south poles.

AB - All (−1)-homogeneous axisymmetric no-swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus north and south poles have been classified in our earlier work as a four dimensional surface with boundary. In this paper, we establish near the no-swirl solution surface existence, non-existence and uniqueness results on (−1)-homogeneous axisymmetric solutions with nonzero swirl which are smooth on the unit sphere minus north and south poles.

KW - Existence

KW - Homogeneous solutions

KW - Isolated singularities

KW - Stationary Navier-Stokes equations

KW - Uniqueness

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