Now showing items 1-20 of 25

• #### Asymptotic models for free boundary flow in porous media ﻿

(Physica D, 2019)
We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ...
• #### Convex Integration Arising in the Modelling of Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations ﻿

(Journal of Nonlinear Science, 2019-03-30)
We study convex integration solutions in the context of the modelling of shape-memory alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop- erties: Firstly, we relate the maximal ...
• #### Defects in Nematic Shells: a Gamma-convergence discrete-to-continuum approach ﻿

(Archive for Rational Mechanics and Analysis, 2018-07)
In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment ...
• #### Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system ﻿

(Discrete and Continuous Dynamical Systems - Series A, 2017-07-15)
We consider a system describing the dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ...
• #### Dimension reduction for the micromagnetic energy functional on curved thin films ﻿

(2016-12-14)
Micromagnetic con gurations of the vortex and onion type have beenwidely studied in the context of planar structures. Recently a signi cant interest to micromagnetic curved thin lms has appeared. In particular, thin ...
• #### Dispersive effects of weakly compressible and fast rotating inviscid fluids ﻿

(Discrete and Continuous Dynamical Systems - Series A, 2017-08)
We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $H^s \left( \mathbb{R}^3 \right), s>5/2$. ...
• #### Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals ﻿

(Archive for Rational Mechanics and Analysis, 2018-08-10)
We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion equation for the ...
• #### The excluded volume of two-dimensional convex bodies: shape reconstruction and non-uniqueness ﻿

(Journal of Physics A: Mathematical and Theoretical, 2019-02-05)
In the Onsager model of one-component hard-particle systems, the entire phase behaviour is dictated by a function of relative orientation, which represents the amount of space excluded to one particle by another at this ...
• #### Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals ﻿

(Journal of Differential Equations, 2017-10-02)
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 Navier-Stokes system. We study the energy law ...
• #### A Global well-posedness result for the Rosensweig system of ferrofluids ﻿

(Rev. Mat. Iberoam., 2019)
In this Paper we study a Bloch-Torrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of Leray-Hopf solutions of this ...
• #### Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity ﻿

(Revista Matemática Iberoamericana, 2017-07)
We prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ...
• #### Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation ﻿

(Mathematical Models and Methods in Applied Sciences, 2016-12-31)
We consider the two-dimensional Landau-de Gennes energy with several elastic constants, subject to general $k$-radially symmetric boundary conditions. We show that for generic elastic constants the critical points consistent ...
• #### On a hyperbolic system arising in liquid crystal modelling ﻿

(Journal of Hyperbolic Differential Equations, 2017-11)
We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ...
• #### On the controllability of Partial Differential Equations involving non-local terms and singular potentials ﻿

(2016-12-12)
In this thesis, we investigate controllability and observability properties of Partial Differential Equations describing various phenomena appearing in several fields of the applied sciences such as elasticity theory, ...
• #### On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids ﻿

(Journal of Differential Equations, 2018-09)
We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...
• #### On the influence of gravity on density-dependent incompressible periodic fluids ﻿

(J. Differential Equations, 2019)
The present work is devoted to the analysis of density-dependent, incompressible fluids in a 3D torus, when the Froude number $\varepsilon$ goes to zero. We consider the very general case where the initial data do not have ...
• #### Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations ﻿

(Journal of Biological Dynamics, 2016-09-01)
The Lotka-Volterra model is a differential system of two coupled equations representing the interaction of two species: a prey one and a predator one. We formulate an optimal control problem adding the effect of hunting ...
• #### Order Reconstruction for neatics on squares with isotropic inclusions: A Landau-de Gennes study ﻿

(SIAM Journal on Applied Mathematics, 2019-03-30)
e study a modified Landau-de Gennes model for nematic liq- uid crystals, where the elastic term is assumed to be of subquadratic growth in the gradient. We analyze the behaviour of global minimizers in two- and three-dimensional ...
• #### Partial regularity and smooth topology-preserving approximations of rough domains ﻿

(Calculus of Variations and Partial Differential Equations, 2017-01-01)
For a bounded domain $\Omega\subset\mathbb{R}^m, m\geq 2,$ of class $C^0$, the properties are studied of fields of `good directions', that is the directions with respect to which $\partial\Omega$ can be locally represented ...
• #### Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals ﻿

(Proceedings of the Royal Society A-Mathematical, Physical and Engineering Sciences, 2018-02-14)
We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in ...