Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit
The main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact appro...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2018-10-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2018-0094 |
| _version_ | 1823947285381251072 |
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| author | Fan Xiaoting Wang Shu Xu Wen-Qing Liu Mingshuo |
| author_facet | Fan Xiaoting Wang Shu Xu Wen-Qing Liu Mingshuo |
| author_sort | Fan Xiaoting |
| collection | DOAJ |
| description | The main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates O(ε32)$O(\varepsilon^{\frac{3}{2}})$ and O(ε2). |
| first_indexed | 2024-12-17T09:44:00Z |
| format | Article |
| id | doaj.art-559a8f89e8c946a3bcc1fdd33dcee76d |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-17T09:44:00Z |
| publishDate | 2018-10-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-559a8f89e8c946a3bcc1fdd33dcee76d2022-12-21T21:53:48ZengDe GruyterOpen Mathematics2391-54552018-10-011611145116010.1515/math-2018-0094math-2018-0094Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limitFan Xiaoting0Wang Shu1Xu Wen-Qing2Liu Mingshuo3College of Applied Sciences, Beijing University of Technology, Beijing100124, ChinaCollege of Applied Sciences, Beijing University of Technology, Beijing100124, ChinaDepartment of Mathematics and Statistics, California State University, Long Beach, CA 90840, USACollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qian Wan Gang, Road 579, Huangdao District, Qingdao266590, ChinaThe main purpose of this paper is to study the initial layer problem and the infinite Prandtl number limit of Rayleigh-Bénard convection with an ill prepared initial data. We use the asymptotic expansion methods of singular perturbation theory and the two-time-scale approach to obtain an exact approximating solution and the convergence rates O(ε32)$O(\varepsilon^{\frac{3}{2}})$ and O(ε2).https://doi.org/10.1515/math-2018-0094boussinesq systemrayleigh-bénard convectioninfinite prandtl number limitinitial layersasymptotic expansiontwo-time-scale approach35b2535b4035k57 |
| spellingShingle | Fan Xiaoting Wang Shu Xu Wen-Qing Liu Mingshuo Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit Open Mathematics boussinesq system rayleigh-bénard convection infinite prandtl number limit initial layers asymptotic expansion two-time-scale approach 35b25 35b40 35k57 |
| title | Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit |
| title_full | Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit |
| title_fullStr | Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit |
| title_full_unstemmed | Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit |
| title_short | Initial layer problem of the Boussinesq system for Rayleigh-Bénard convection with infinite Prandtl number limit |
| title_sort | initial layer problem of the boussinesq system for rayleigh benard convection with infinite prandtl number limit |
| topic | boussinesq system rayleigh-bénard convection infinite prandtl number limit initial layers asymptotic expansion two-time-scale approach 35b25 35b40 35k57 |
| url | https://doi.org/10.1515/math-2018-0094 |
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