A Review of results on axially symmetric Navier-Stokes equations, with addendum by X. Pan and Q. S. Zhang
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arXiv
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866910551012016128 |
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| author | Zhang, Qi S. |
| author_facet | Zhang, Qi S. |
| contents | In this paper, we give a brief survey of recent results on axially symmetric Navier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property for ancient solutions, decay and vanishing of stationary solutions. Some discussions also touch on the full 3 dimensional equations. Two results, closing of the scaling gap for ASNS and vanishing of homogeneous D solutions in 3 dimensional slabs will be described in more detail. In the addendum, two new results in the 3rd category will also be presented, which are generalizations of recently published results by the author and coauthors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_04905 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A Review of results on axially symmetric Navier-Stokes equations, with addendum by X. Pan and Q. S. Zhang Zhang, Qi S. Analysis of PDEs 35Q30, 76N10 In this paper, we give a brief survey of recent results on axially symmetric Navier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property for ancient solutions, decay and vanishing of stationary solutions. Some discussions also touch on the full 3 dimensional equations. Two results, closing of the scaling gap for ASNS and vanishing of homogeneous D solutions in 3 dimensional slabs will be described in more detail. In the addendum, two new results in the 3rd category will also be presented, which are generalizations of recently published results by the author and coauthors. |
| title | A Review of results on axially symmetric Navier-Stokes equations, with addendum by X. Pan and Q. S. Zhang |
| topic | Analysis of PDEs 35Q30, 76N10 |
| url | https://arxiv.org/abs/2101.04905 |