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Artículo
Error analysis of a subgrid eddy viscosity multi-scale discretization of the Navier-Stokes equations
(Sociedad Española de Matemática Aplicada, 2012-08-14)
We propose a finite element discretization of the Navier–Stokes equations that relies on the variational multi-scale approach together with the addition of a Smagorinsky type viscosity, in order to take into account ...
Artículo
Analysis of a coupled fluid-structure model with applications to hemodynamics
(Society for Industrial and Applied Mathematics, 2016)
We propose and analyze a simplified fluid-structure coupled model for flows with compliant walls. As in [F. Nobile and C. Vergara, SIAM J. Sci. Comput., 30 (2008), pp. 731-763], the wall reaction to the fluid is modeled ...
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
A variational finite element model for Large-Eddy simulations of turbulent flows
(Springer, 2013-09)
We introduce a new Large Eddy Simulation model in a channel, based on the projection on finite element spaces as filtering operation in its variational form, for a given triangulation {Th}h>0. The eddy viscosity is expressed ...
Artículo
Pullback Attractors for 2D-Navier-Stokes Equations with Delays In Continuous and Sub-Linear Operators
(American Institute of Mathematical Sciences, 2010)
We obtain a result of existence of solutions to the 2D-Navier-Stokes model with delays, when the forcing term containing the delay is sub-linear and only continuous. As a consequence of the continuity assumption the ...
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
Two scenarios on a potential smoothness breakdown for the three-dimensional Navier-Stokes equations
(Cornell University, 2018)
In this paper we construct two families of initial data being arbitrarily large under any scaling-invariant norm for which their corresponding weak solution to the three-dimensional Navier- Stokes equations become smooth ...