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On the motion of a large number of small rigid bodies in a viscous incompressible fluid

Feireisl, E.; Roy, A.; Zarnescu, A. (2022-01-01)

We consider the motion of N rigid bodies – compact sets (S1 ε ,· · · ,SN ε )ε>0 – immersed in a viscous incompressible fluid contained in a domain in the Euclidean space Rd , d = 2,3. We show the fluid flow is not infl...

Colloidal homogenization for the hydrodynamics of nematic liquid crystals

De Anna, F.; Schlömerkemper, A.; Zarnescu, A. (2024-01-01)

This paper analytically explores a simplified model for the hydrodynamics of nematic liquid crystal colloids. We integrate a Stokes equation for the velocity field with a Ginzburg–Landau transported heat flow for the dir...

Boundary layers for the upper-convected Beris–Edwards model of nematic liquid crystals

De Anna, F.; Kortum, J.; Zarnescu, A. (2025-01-01)

In this paper, we derive and analyze a set of Prandtl-type equations for the boundary layers in nematic liquid crystals. We focus on a two-dimensional model where the hydrodynamics are governed by the Beris–Edwards equatio...

ASYMPTOTIC BEHAVIOR OF THE FREE INTERFACE FOR ENTIRE VECTOR MINIMIZERS IN PHASE TRANSITIONS

Alikakos, N.; Geng, Z.; Zarnescu, A. (2021-01-01)

We study globally bounded entire minimizers u : Rn → Rm of Allen-Cahn systems for potentials W ≥ 0 with {W = 0}= {a1, ..., aN } and W (u) ∼ |u− ai|α near u = ai, 0 < α < 2. Such solutions are, over large regions, identical...