Strong well-posedness of a fluid--poro-viscoelastic interaction problem: An approach by Spectral analysis
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917548057952256 |
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| author | Binz, Tim Hieber, Matthias Roy, Arnab |
| author_facet | Binz, Tim Hieber, Matthias Roy, Arnab |
| contents | This article investigates a coupled viscoelastic Navier--Stokes--Biot system describing the interaction between an incompressible viscous fluid and a poro--viscoelastic medium in three spatial dimensions. The coupling between the fluid and the porous medium is realized through Beavers--Joseph--Saffman type interface conditions. Using spectral analysis, it is proved that the coupled system admits a unique, strong, global solution for small initial data. In addition, a Serrin--type blow-up criterion is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_31322 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Strong well-posedness of a fluid--poro-viscoelastic interaction problem: An approach by Spectral analysis Binz, Tim Hieber, Matthias Roy, Arnab Analysis of PDEs 35Q35, 76D05, 76S05, 74F10 This article investigates a coupled viscoelastic Navier--Stokes--Biot system describing the interaction between an incompressible viscous fluid and a poro--viscoelastic medium in three spatial dimensions. The coupling between the fluid and the porous medium is realized through Beavers--Joseph--Saffman type interface conditions. Using spectral analysis, it is proved that the coupled system admits a unique, strong, global solution for small initial data. In addition, a Serrin--type blow-up criterion is established. |
| title | Strong well-posedness of a fluid--poro-viscoelastic interaction problem: An approach by Spectral analysis |
| topic | Analysis of PDEs 35Q35, 76D05, 76S05, 74F10 |
| url | https://arxiv.org/abs/2605.31322 |