2019
DOI: 10.3934/dcds.2019300
|View full text |Cite
|
Sign up to set email alerts
|

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

Abstract: Dedicated to Luis Caffarelli on his 70th birthday, with admiration and friendship. AbstractAll (−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 solut… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
4
1

Citation Types

1
9
0

Year Published

2021
2021
2024
2024

Publication Types

Select...
6

Relationship

1
5

Authors

Journals

citations
Cited by 12 publications
(10 citation statements)
references
References 7 publications
1
9
0
Order By: Relevance
“…In this work, stronger vorticity events are observed, with vorticity isosurfaces being blob-like and zones of large dissipation being colocated with zones of large vorticity. This colocation of the large vorticity and large dissipation zones is also observed in the stationary singular solutions of Li, Li & Yan (2018). The discrepancy between our experimental result and these numerical results may, however, be a spurious effect since it is known that they are very sensitive to the spatial and temporal resolution (Yeung, Sreenivasan & Pope 2018).…”
Section: Discussionsupporting
confidence: 69%
“…In this work, stronger vorticity events are observed, with vorticity isosurfaces being blob-like and zones of large dissipation being colocated with zones of large vorticity. This colocation of the large vorticity and large dissipation zones is also observed in the stationary singular solutions of Li, Li & Yan (2018). The discrepancy between our experimental result and these numerical results may, however, be a spurious effect since it is known that they are very sensitive to the spatial and temporal resolution (Yeung, Sreenivasan & Pope 2018).…”
Section: Discussionsupporting
confidence: 69%
“…It was also proved there that there exists a curve of axisymmetric solutions with nonzero swirl emanating from every point in the interior and one part of the boundary of the surface of no-swirl solutions, while there is no such curve from any point on the other part of the boundary. Uniqueness results of nonzero swirl solutions near the no-swirl solution surface were also given in [4]. Our main result in this paper is the classification of all (-1)-homogeneous, axisymmetric no-swirl solutions of (1) which are smooth on S 2 \ {S, N }, where S is the south pole and N is the north pole.…”
Section: Introductionmentioning
confidence: 82%
“…We are interested in analyzing solutions which are smooth on S 2 minus finite points. We have classified in [4] all axisymmetric no-swirl solutions with one singularity at the south pole. They form a two dimensional surface with boundary in appropriate function spaces.…”
Section: Introductionmentioning
confidence: 99%
See 2 more Smart Citations