Slow traveling-wave solutions for the generalized surface quasi-geostrophic equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917255464353792 |
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| author | Cao, Daomin Lai, Shanfa Qin, Guolin |
| author_facet | Cao, Daomin Lai, Shanfa Qin, Guolin |
| contents | In this paper, we systematically study the existence, asymptotic behaviors, uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds for the generalized surface quasi-geostrophic (gSQG) equation. Firstly we obtain the existence of a new family of global solutions via the variational method. Secondly we show the uniqueness of maximizers under our variational setting. Thirdly by using the variational framework, the uniqueness of maximizers and a concentration-compactness principle we establish some stability theorems. Moreover, after a suitable transformation, these solutions constitute the desingularization of traveling point vortex pairs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_00368 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Slow traveling-wave solutions for the generalized surface quasi-geostrophic equation Cao, Daomin Lai, Shanfa Qin, Guolin Analysis of PDEs In this paper, we systematically study the existence, asymptotic behaviors, uniqueness, and nonlinear orbital stability of traveling-wave solutions with small propagation speeds for the generalized surface quasi-geostrophic (gSQG) equation. Firstly we obtain the existence of a new family of global solutions via the variational method. Secondly we show the uniqueness of maximizers under our variational setting. Thirdly by using the variational framework, the uniqueness of maximizers and a concentration-compactness principle we establish some stability theorems. Moreover, after a suitable transformation, these solutions constitute the desingularization of traveling point vortex pairs. |
| title | Slow traveling-wave solutions for the generalized surface quasi-geostrophic equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2301.00368 |