Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum
In this article, we investigate an initial and boundary value problem for a class of compressible non-Newtonian fluids, provided the initial energy is small and the initial density containing the vacuum state is allowed. For $p>2$, we obtain the existence and uniqueness of the global strong solut...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-02-01
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| Series: | Comptes Rendus. Mécanique |
| Subjects: | |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.68/ |
| _version_ | 1827785174477176832 |
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| author | Xu, Jianjun Yuan, Hongjun |
| author_facet | Xu, Jianjun Yuan, Hongjun |
| author_sort | Xu, Jianjun |
| collection | DOAJ |
| description | In this article, we investigate an initial and boundary value problem for a class of compressible non-Newtonian fluids, provided the initial energy is small and the initial density containing the vacuum state is allowed. For $p>2$, we obtain the existence and uniqueness of the global strong solution for this problem in a one-dimensional bounded interval. |
| first_indexed | 2024-03-11T16:15:19Z |
| format | Article |
| id | doaj.art-91e5fb9b69464646a8f8bb2de5f659a6 |
| institution | Directory Open Access Journal |
| issn | 1873-7234 |
| language | English |
| last_indexed | 2024-03-11T16:15:19Z |
| publishDate | 2021-02-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj.art-91e5fb9b69464646a8f8bb2de5f659a62023-10-24T14:20:53ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342021-02-013491294110.5802/crmeca.6810.5802/crmeca.68Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuumXu, Jianjun0Yuan, Hongjun1Institute of Mathematics, Jilin University, Changchun 130012, PR ChinaInstitute of Mathematics, Jilin University, Changchun 130012, PR ChinaIn this article, we investigate an initial and boundary value problem for a class of compressible non-Newtonian fluids, provided the initial energy is small and the initial density containing the vacuum state is allowed. For $p>2$, we obtain the existence and uniqueness of the global strong solution for this problem in a one-dimensional bounded interval.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.68/Non-Newtonian fluidGlobal strong solutionA priori estimateExistence and uniquenessVacuum |
| spellingShingle | Xu, Jianjun Yuan, Hongjun Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum Comptes Rendus. Mécanique Non-Newtonian fluid Global strong solution A priori estimate Existence and uniqueness Vacuum |
| title | Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum |
| title_full | Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum |
| title_fullStr | Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum |
| title_full_unstemmed | Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum |
| title_short | Existence and uniqueness of global strong solutions for a class of non-Newtonian fluids with small initial energy and vacuum |
| title_sort | existence and uniqueness of global strong solutions for a class of non newtonian fluids with small initial energy and vacuum |
| topic | Non-Newtonian fluid Global strong solution A priori estimate Existence and uniqueness Vacuum |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.68/ |
| work_keys_str_mv | AT xujianjun existenceanduniquenessofglobalstrongsolutionsforaclassofnonnewtonianfluidswithsmallinitialenergyandvacuum AT yuanhongjun existenceanduniquenessofglobalstrongsolutionsforaclassofnonnewtonianfluidswithsmallinitialenergyandvacuum |