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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
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
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 ...
Artículo
Weak time regularity and uniqueness for a Q-Tensor model
(Society for Industrial and Applied Mathematics, 2014)
The coupled Navier-Stokes and Q-Tensor system is one of the models used to describe the behavior of the nematic liquid crystals. The existence of weak solutions and a uniqueness criteria have been already studied (see [11] ...
Artículo
Regularity and time-periodicity for a nematic liquid crystal model
(Elsevier, 2009-07)
In this paper two main results are obtained for a nematic liquid crystal model with timedependent boundary Dirichlet data for the orientation of the crystal molecules. First, the initial-boundary problem is considered, ...
Artículo
On a double penalized smectic-A model
(American Institute of Mathematical Sciences, 2012-12)
In smectic-A liquid crystals a unity director vector n appear, modeling an average preferential direction of the molecules and also the normal vector of the layer configuration. In the E’s model [5] W. E. Nonlinear Continuum ...
Artículo
Reproductivity for a nematic liquid crystal model
(2006-11)
In this paper we prove existence of weak solution with the reproductivity in time property, for a penalized PDE's system related to a nematic liquid crystal model. This problem is relatively explicit when time-independent ...