Capillarity driven Stokes flow: the one-phase problem as small viscosity limit
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917648066936832 |
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| author | Prokert, Georg Matioc, Bogdan-Vasile |
| author_facet | Prokert, Georg Matioc, Bogdan-Vasile |
| contents | We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear parabolic evolution problem for the function that parameterizes the boundary of the fluid with the nonlinearities expressed in terms of singular integrals. We prove well-posedness of the problem in the subcritical Sobolev spaces $H^s(\mathbb{R})$ up to critical regularity, and establish parabolic smoothing properties for the solutions. Moreover, we identify the problem as the singular limit of the two-phase quasistationary Stokes flow when the viscosity of one of the fluids vanishes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_13376 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Capillarity driven Stokes flow: the one-phase problem as small viscosity limit Prokert, Georg Matioc, Bogdan-Vasile Analysis of PDEs 76D07, 35R37, 35K55 We consider the quasistationary Stokes flow that describes the motion of a two-dimensional fluid body under the influence of surface tension effects in an unbounded, infinite-bottom geometry. We reformulate the problem as a fully nonlinear parabolic evolution problem for the function that parameterizes the boundary of the fluid with the nonlinearities expressed in terms of singular integrals. We prove well-posedness of the problem in the subcritical Sobolev spaces $H^s(\mathbb{R})$ up to critical regularity, and establish parabolic smoothing properties for the solutions. Moreover, we identify the problem as the singular limit of the two-phase quasistationary Stokes flow when the viscosity of one of the fluids vanishes. |
| title | Capillarity driven Stokes flow: the one-phase problem as small viscosity limit |
| topic | Analysis of PDEs 76D07, 35R37, 35K55 |
| url | https://arxiv.org/abs/2209.13376 |