30 citations · 32 across the 5 of their papers we have counts for
9 papers
Colloidal Homogenisation for the Hydrodynamics of Nematic Liquid Crystals
Francesco De Anna, Anja Schloemerkemper, Arghir Zarnescu
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-…
Quantitative aspects on the ill-posedness of the Prandtl and hyperbolic Prandtl equations
Francesco De Anna, Joshua Kortum, Stefano Scrobogna
We address a physically-meaningful extension of the Prandtl system, also known as hyperbolic Prandtl equations. We show that the linearised model around a non-monotonic shear flow…
Gevrey-class-3 regularity of the linearised hyperbolic Prandtl system on a strip
Francesco De Anna, Joshua Kortum, Stefano Scrobogna
In the present paper, we address a physically-meaningful extension of the linearised Prandtl equations around a shear flow. Without any structural assumption, it is well-known that…
Uniqueness of weak solutions for the general Ericksen-Leslie system with Ginzburg-Landau penalization in T^2
Francesco De Anna, Hao Wu
The Ericksen-Leslie system is a fundamental hydrodynamic model that describes the evolution of incompressible liquid crystal flows of nematic type. In this paper, we prove the uniq…
Non-isothermal general Ericksen-Leslie system: derivation, analysis and thermodynamics-consistency
Francesco De Anna, Chun Liu
We derive a model describing the evolution of a nematic liquid-crystal material under the action of thermal effects. The first and second laws of thermodynamics lead to an extensio…
Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals
Francesco de Anna, Arghir Zarnescu
We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navi…
Global Weak Solutions for Boussinesq System with Temperature dependent Viscosity and bounded Temperature
Francesco De Anna
In this paper we obtain a result about the global existence of weak solutions for the -dimensional Bussinesq system, with viscosity dependent on temperature. The initial tempera…
A Global 2D Well-Posedness Result on the Order Tensor Liquid Crystal Theory
Francesco De Anna
Paicu and Zarnescu have studied an order tensor system which describes the flow of a liquid crystal. They have proven the existence of weak solutions, the propagation of higher reg…
Uniqueness of Weak Solutions of the Full Coupled Navier-Stokes and Q-Tensor System in 2D
Francesco De Anna, Arghir Zarnescu
This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions…