On desingularization of steady vortex for the lake equations
Abstract In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes a desingularization of a singular vortex. The precise localization of the asymptotic singular vortex is shown to be the deepest position of the lake....
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| Published in | IMA journal of applied mathematics Vol. 87; no. 1; pp. 50 - 79 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford University Press
22.01.2022
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0272-4960 1464-3634 |
| DOI | 10.1093/imamat/hxab042 |
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| Abstract | Abstract
In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes a desingularization of a singular vortex. The precise localization of the asymptotic singular vortex is shown to be the deepest position of the lake. We also study global nonlinear stability for these solutions. Some qualitative and asymptotic properties are also established. |
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| AbstractList | Abstract
In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes a desingularization of a singular vortex. The precise localization of the asymptotic singular vortex is shown to be the deepest position of the lake. We also study global nonlinear stability for these solutions. Some qualitative and asymptotic properties are also established. In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes a desingularization of a singular vortex. The precise localization of the asymptotic singular vortex is shown to be the deepest position of the lake. We also study global nonlinear stability for these solutions. Some qualitative and asymptotic properties are also established. |
| Author | Zhan, Weicheng Zou, Changjun Cao, Daomin |
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| Cites_doi | 10.1007/s00205-004-0339-0 10.1512/iumj.1996.45.1199 10.1215/S0012-7094-80-04743-2 10.1007/s00205-010-0293-y 10.1016/j.jfa.2004.04.005 10.1080/03605308308820293 10.1007/BFb0088744 10.1137/18M1170169 10.1016/0362-546X(80)90083-8 10.1007/s00205-013-0692-y 10.1007/BF02797686 10.1016/j.aim.2014.09.027 10.1017/S0022112099008393 10.1007/s00205-013-0647-3 10.1016/j.matpur.2019.05.011 10.1016/0022-1236(73)90051-7 10.1007/s00220-020-03742-z 10.1007/BF01450739 10.1007/s00205-019-01448-8 10.1007/BF00281469 10.1016/0021-8928(65)90119-X 10.1112/jlms/s2-21.2.329 10.1017/S0022112097006721 |
| ContentType | Journal Article |
| Copyright | The Author(s) 2021. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. 2021 |
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| Keywords | steady vortex solutions maximizer elliptic equations desingularization variational method |
| Language | English |
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In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes a... In this paper, we constructed a family of steady vortex solutions for the lake equations with a general vorticity function, which constitutes a... |
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