On the global well-posedness of interface dynamics for gravity Stokes flow
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929256068546560 |
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| author | Gancedo, Francisco Granero-Belinchón, Rafael Salguero, Elena |
| author_facet | Gancedo, Francisco Granero-Belinchón, Rafael Salguero, Elena |
| contents | In this paper we establish the global-in-time well-posedness for an arbitrary $C^{1+γ}$, $0<γ<1$, initial internal wave for the free boundary gravity Stokes system in two dimensions. This classical well-posedness result is complemented with a weak solvability result in the case of $C^γ$ or Lipschitz interfaces. Furthermore, we also propose and study several one-dimensional models that capture different features of the full internal wave problem for the gravity Stokes system and show that all of them present finite time singularities. This fact evidences the fine structure of the non-linearity in the full system that allows for the free boundary problem to be globally well-posed while simplifications of it blow-up in finite time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_15593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the global well-posedness of interface dynamics for gravity Stokes flow Gancedo, Francisco Granero-Belinchón, Rafael Salguero, Elena Analysis of PDEs 35Q35, 76D03, 76D07 In this paper we establish the global-in-time well-posedness for an arbitrary $C^{1+γ}$, $0<γ<1$, initial internal wave for the free boundary gravity Stokes system in two dimensions. This classical well-posedness result is complemented with a weak solvability result in the case of $C^γ$ or Lipschitz interfaces. Furthermore, we also propose and study several one-dimensional models that capture different features of the full internal wave problem for the gravity Stokes system and show that all of them present finite time singularities. This fact evidences the fine structure of the non-linearity in the full system that allows for the free boundary problem to be globally well-posed while simplifications of it blow-up in finite time. |
| title | On the global well-posedness of interface dynamics for gravity Stokes flow |
| topic | Analysis of PDEs 35Q35, 76D03, 76D07 |
| url | https://arxiv.org/abs/2402.15593 |