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Artículo
Numerical methods for solving the Cahn-Hilliard equation and its applicability to related Energy-based models
(Springer, 2015-04)
In this paper, we review some numerical methods presented in the literature in the last years to approximate the Cahn-Hilliard equation. Our aim is to compare the main properties of each one of the approaches to try to ...
Artículo
Stabilized schemes for the hydrostatic Stokes equations
(Society for Industrial and Applied Mathematics, 2015)
Some new stable finite element (FE) schemes are presented for the hydrostatic Stokes system or primitive equations of the ocean. It is known that the stability of the mixed formulation approximation for primitive equations ...
Artículo
Unconditionally energy stable fully discrete schemes for a chemo-repulsion model
(American Mathematical Society, 2019-09)
This work is devoted to studying unconditionally energy stable and mass-conservative numerical schemes for the following repulsive-productive chemotaxis model: find u ≥ 0, the cell density, and v ≥ 0, the chemical ...
Artículo
Convergence to equilibrium of global weak solutions for a Cahn-Hilliard-Navier-Stokes vesicle model
(Springer, 2019-08)
In this paper, we introduce a model describing the dynamic of vesicle membranes within an incompressible viscous fluid in 3D domains. The system consists of the NavierStokes equations, with an extra stress tensor depending ...
Artículo
Convergence to equilibrium for smectic-A liquid crystals in 3D domains without constraints for the viscosity
(Elsevier, 2014-06)
In this paper, we focus on a smectic-A liquid crystal model in 3D domains, and obtain three main results: the proof of an adequate Lojasiewicz-Simon inequality by using an abstract result; the rigorous proof (via a Galerkin ...
Artículo
An overview on numerical analyses of nematic liquid crystal flows
(Springer, 2011-09)
The purpose of this work is to provide an overview of the most recent numerical developments in the field of nematic liquid crystals. The Ericksen-Leslie equations govern the motion of a nematic liquid crystal. This system, ...
Artículo
Weak solutions for an initial-boundary Q-Tensor problem related to liquid crystals
(Elsevier, 2015-01)
The coupled Navier-Stokes and Q-Tensor system is considered in a bounded three-dimensional domain under homogeneous Dirichlet boundary conditions for the velocity u and either nonhomogeneous Dirichlet or homogeneous Neumann ...
Artículo
Approximation of Smectic-A liquid crystals
(Elsevier, 2015-06-15)
In this paper, we present energy-stable numerical schemes for a Smectic-A liquid crystal model. This model involve the hydrodynamic velocity-pressure macroscopic variables (u, p) and the microscopic order parameter of ...
Artículo
A review on mathematical analysis for nematic and smectic-A liquid crystal models
(Cambridge University Press, 2014-02)
We review the mathematical analysis of some uniaxial, liquid crystal phases. First, we state the models for the two di fferent studied phases: nematic and smectic-A liquid crystals. The spatial and temporal pro les of the ...
Artículo
Global in time solution and time-periodicity for a smectic-A liquid crystal model
(American Institute of Mathematical Sciences, 2010)
In this paper some results are obtained for a smectic-A liquid crystal model with time-dependent boundary Dirichlet data for the so-called layer variable φ (the level sets of φ describe the layer structure of the smectic-A ...