Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D
This paper shows the existence, uniqueness, and asymptotic behavior in time of regular solutions (a la Ladyzhenskaya) to the Bénard problem for a heat-conducting fluid model generalizing the classical Oberbeck–Boussinesq one. The novelty of this model, introduced by Corli and Passerini, 2019, and Pa...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2020/9610689 |
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| _version_ | 1832568562958467072 |
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| author | Arianna Passerini |
| author_facet | Arianna Passerini |
| author_sort | Arianna Passerini |
| collection | DOAJ |
| description | This paper shows the existence, uniqueness, and asymptotic behavior in time of regular solutions (a la Ladyzhenskaya) to the Bénard problem for a heat-conducting fluid model generalizing the classical Oberbeck–Boussinesq one. The novelty of this model, introduced by Corli and Passerini, 2019, and Passerini and Ruggeri, 2014, consists in allowing the density of the fluid to also depend on the pressure field, which, as shown by Passerini and Ruggeri, 2014, is a necessary request from a thermodynamic viewpoint when dealing with convective problems. This property adds to the problem a rather interesting mathematical challenge that is not encountered in the classical model, thus requiring a new approach for its resolution. |
| format | Article |
| id | doaj-art-46730f8838d9463ab35f0b5bb708a0f1 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-46730f8838d9463ab35f0b5bb708a0f12025-02-03T00:58:49ZengWileyInternational Journal of Differential Equations1687-96431687-96512020-01-01202010.1155/2020/96106899610689Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3DArianna Passerini0Department of Mathematics and Computer Science, University of Ferrara, Via Machiavelli 30, 40121 Ferrara, ItalyThis paper shows the existence, uniqueness, and asymptotic behavior in time of regular solutions (a la Ladyzhenskaya) to the Bénard problem for a heat-conducting fluid model generalizing the classical Oberbeck–Boussinesq one. The novelty of this model, introduced by Corli and Passerini, 2019, and Passerini and Ruggeri, 2014, consists in allowing the density of the fluid to also depend on the pressure field, which, as shown by Passerini and Ruggeri, 2014, is a necessary request from a thermodynamic viewpoint when dealing with convective problems. This property adds to the problem a rather interesting mathematical challenge that is not encountered in the classical model, thus requiring a new approach for its resolution.http://dx.doi.org/10.1155/2020/9610689 |
| spellingShingle | Arianna Passerini Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D International Journal of Differential Equations |
| title | Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D |
| title_full | Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D |
| title_fullStr | Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D |
| title_full_unstemmed | Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D |
| title_short | Bénard Problem for Slightly Compressible Fluids: Existence and Nonlinear Stability in 3D |
| title_sort | benard problem for slightly compressible fluids existence and nonlinear stability in 3d |
| url | http://dx.doi.org/10.1155/2020/9610689 |
| work_keys_str_mv | AT ariannapasserini benardproblemforslightlycompressiblefluidsexistenceandnonlinearstabilityin3d |