On the uniqueness for weak solutions of steady double-phase fluids
We consider a double-phase non-Newtonian fluid, described by a stress tensor which is the sum of a p-Stokes and a q-Stokes stress tensor, with 1 < p<2 < q<∞. For a wide range of parameters (p, q), we prove the uniqueness of small solutions. We use the p < 2 features to obtain quadrati...
| Published in: | Advances in Nonlinear Analysis |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2021-09-01
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| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2020-0196 |
| _version_ | 1852686761756459008 |
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| author | Abdelwahed Mohamed Berselli Luigi C. Chorfi Nejmeddine |
| author_facet | Abdelwahed Mohamed Berselli Luigi C. Chorfi Nejmeddine |
| author_sort | Abdelwahed Mohamed |
| collection | DOAJ |
| container_title | Advances in Nonlinear Analysis |
| description | We consider a double-phase non-Newtonian fluid, described by a stress tensor which is the sum of a p-Stokes and a q-Stokes stress tensor, with 1 < p<2 < q<∞. For a wide range of parameters (p, q), we prove the uniqueness of small solutions. We use the p < 2 features to obtain quadratic-type estimates for the stress-tensor, while we use the improved regularity coming from the term with q > 2 to justify calculations for weak solutions. Results are obtained through a careful use of the symmetries of the convective term and are also valid for rather general (even anisotropic) stress-tensors. |
| format | Article |
| id | doaj-art-e7c3e89a04e34c2685aa4bf98a1dffae |
| institution | Directory of Open Access Journals |
| issn | 2191-9496 2191-950X |
| language | English |
| publishDate | 2021-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| spelling | doaj-art-e7c3e89a04e34c2685aa4bf98a1dffae2025-08-19T21:26:18ZengDe GruyterAdvances in Nonlinear Analysis2191-94962191-950X2021-09-0111145446810.1515/anona-2020-0196On the uniqueness for weak solutions of steady double-phase fluidsAbdelwahed Mohamed0Berselli Luigi C.1Chorfi Nejmeddine2Department of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh11451, Saudi ArabiaDipartimento di Matematica Università di Pisa Via F. Buonarroti 1/c, PisaI-56127, ItalyDepartment of Mathematics, College of Sciences, King Saud University, P.O. Box 2455, Riyadh11451, Saudi ArabiaWe consider a double-phase non-Newtonian fluid, described by a stress tensor which is the sum of a p-Stokes and a q-Stokes stress tensor, with 1 < p<2 < q<∞. For a wide range of parameters (p, q), we prove the uniqueness of small solutions. We use the p < 2 features to obtain quadratic-type estimates for the stress-tensor, while we use the improved regularity coming from the term with q > 2 to justify calculations for weak solutions. Results are obtained through a careful use of the symmetries of the convective term and are also valid for rather general (even anisotropic) stress-tensors.https://doi.org/10.1515/anona-2020-0196uniquenessdouble-phasesteady motionnon-newtonian fluid76a0535j6235q3035j2535j55 |
| spellingShingle | Abdelwahed Mohamed Berselli Luigi C. Chorfi Nejmeddine On the uniqueness for weak solutions of steady double-phase fluids uniqueness double-phase steady motion non-newtonian fluid 76a05 35j62 35q30 35j25 35j55 |
| title | On the uniqueness for weak solutions of steady double-phase fluids |
| title_full | On the uniqueness for weak solutions of steady double-phase fluids |
| title_fullStr | On the uniqueness for weak solutions of steady double-phase fluids |
| title_full_unstemmed | On the uniqueness for weak solutions of steady double-phase fluids |
| title_short | On the uniqueness for weak solutions of steady double-phase fluids |
| title_sort | on the uniqueness for weak solutions of steady double phase fluids |
| topic | uniqueness double-phase steady motion non-newtonian fluid 76a05 35j62 35q30 35j25 35j55 |
| url | https://doi.org/10.1515/anona-2020-0196 |
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