Analysis of a Navier-Stokes phase-field crystal system
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913316607098880 |
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| author | Cavaterra, Cecilia Grasselli, Maurizio Mehmood, Muhammed Ali Voso, Riccardo |
| author_facet | Cavaterra, Cecilia Grasselli, Maurizio Mehmood, Muhammed Ali Voso, Riccardo |
| contents | We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier-Stokes equations for the volume averaged velocity coupled with the so-called Phase-Field Crystal equation for the density deviation. Considering this system in a periodic domain and assuming that the viscosity as well as the mobility depend on the density deviation, we first prove the existence of a weak solution in dimension three. Then, in dimension two, we establish the existence of a (unique) strong solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10431 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of a Navier-Stokes phase-field crystal system Cavaterra, Cecilia Grasselli, Maurizio Mehmood, Muhammed Ali Voso, Riccardo Analysis of PDEs 35Q35, 76T20 We consider an evolution system modeling a flow of colloidal particles which are suspended in an incompressible fluid and accounts for colloidal crystallization. The system consists of the Navier-Stokes equations for the volume averaged velocity coupled with the so-called Phase-Field Crystal equation for the density deviation. Considering this system in a periodic domain and assuming that the viscosity as well as the mobility depend on the density deviation, we first prove the existence of a weak solution in dimension three. Then, in dimension two, we establish the existence of a (unique) strong solution. |
| title | Analysis of a Navier-Stokes phase-field crystal system |
| topic | Analysis of PDEs 35Q35, 76T20 |
| url | https://arxiv.org/abs/2404.10431 |