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...
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| Main Authors: | , , |
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| Format: | article |
| Language: | EN |
| Published: |
De Gruyter
2021
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| Subjects: | |
| Online Access: | https://doaj.org/article/e7c3e89a04e34c2685aa4bf98a1dffae |
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| Summary: | 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. |
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