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arXiv · 2404.10431

Analysis of a Navier-Stokes phase-field crystal system

Cecilia Cavaterra·Maurizio Grasselli·Muhammed Ali Mehmood·Riccardo Voso
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Abstract

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.

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Cecilia Cavaterra, Maurizio Grasselli, Muhammed Ali Mehmood, Riccardo Voso. 2024-04-16. Analysis of a Navier-Stokes phase-field crystal system. https://arxiv.org/abs/2404.10431

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