Qualitative/quantitative homogenization of some non-Newtonian flows in perforated domains
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909909691400192 |
|---|---|
| author | Höfer, Richard M. Lu, Yong Oschmann, Florian |
| author_facet | Höfer, Richard M. Lu, Yong Oschmann, Florian |
| contents | In this paper, we consider the homogenization of stationary and evolutionary incompressible viscous non-Newtonian flows of Carreau-Yasuda type in domains perforated with a large number of periodically distributed small holes in $\mathbb{R}^{3}$, where the mutual distance between the holes is measured by a small parameter $\varepsilon>0$ and the size of the holes is $\varepsilon^α$ with $α\in (1, 3)$. The Darcy's law is recovered in the limit, thus generalizing the results from https://doi.org/10.1016/0362-546X(94)00285-P and [https://doi.org/10.1016/j.jde.2024.08.021] for $α=1$. Instead of using their restriction operator to derive the estimates of the pressure extension by duality, we use the Bogovski\uı type operator in perforated domains (constructed in [https://doi.org/10.1051/cocv/2016016]) to deduce the uniform estimates of the pressure directly. Moreover, quantitative convergence rates are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_17406 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Qualitative/quantitative homogenization of some non-Newtonian flows in perforated domains Höfer, Richard M. Lu, Yong Oschmann, Florian Analysis of PDEs In this paper, we consider the homogenization of stationary and evolutionary incompressible viscous non-Newtonian flows of Carreau-Yasuda type in domains perforated with a large number of periodically distributed small holes in $\mathbb{R}^{3}$, where the mutual distance between the holes is measured by a small parameter $\varepsilon>0$ and the size of the holes is $\varepsilon^α$ with $α\in (1, 3)$. The Darcy's law is recovered in the limit, thus generalizing the results from https://doi.org/10.1016/0362-546X(94)00285-P and [https://doi.org/10.1016/j.jde.2024.08.021] for $α=1$. Instead of using their restriction operator to derive the estimates of the pressure extension by duality, we use the Bogovski\uı type operator in perforated domains (constructed in [https://doi.org/10.1051/cocv/2016016]) to deduce the uniform estimates of the pressure directly. Moreover, quantitative convergence rates are given. |
| title | Qualitative/quantitative homogenization of some non-Newtonian flows in perforated domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2406.17406 |