Now showing items 1-20 of 35

• #### Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations ﻿

(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 ...
• #### 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, ...
• #### 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 ...
• #### Liquid crystal defects in the Landau–de Gennes theory in two dimensions — Beyond the one-constant approximation ﻿

(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 ...
• #### Partial regularity and smooth topology-preserving approximations of rough domains ﻿

(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 ...
• #### Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity ﻿

(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 ...
• #### Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system ﻿

(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 ...
• #### Dispersive effects of weakly compressible and fast rotating inviscid fluids ﻿

(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 $H^s \left( \mathbb{R}^3 \right), s>5/2$. ...
• #### Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals ﻿

(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 ...
• #### Sphere-valued harmonic maps with surface energy and the K13 problem ﻿

(2017-11)
We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an ...
• #### On a hyperbolic system arising in liquid crystal modelling ﻿

(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 ...
• #### Zero limit of entropic relaxation time for the Shliomis model of ferrofluids ﻿

(2018-02-11)
We construct solutions for the Shilomis model of ferrofluids in a critical space, uniformly in the entropic relaxation time $\tau \in (0, \tau_0)$. This allows us to study the convergence when $\tau\to 0$ for such solutions.
• #### Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals ﻿

(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 ...
• #### Defects in Nematic Shells: a Gamma-convergence discrete-to-continuum approach ﻿

(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 ...
• #### Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals ﻿

(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 ...
• #### On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids ﻿

(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 ...
• #### Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7 ﻿

(2018-09-01)
For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global ...
• #### Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations ﻿

(2018-10)
We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $\mathbb{R}^2$ and Burgers equation in $\mathbb{R}$ with vanishing ...
• #### Models for damped water waves ﻿

(2019)
In this paper we derive some new weakly nonlinear asymptotic models describing viscous waves in deep water with or without surface tension effects. These asymptotic models take into account several different dissipative ...
• #### A Global well-posedness result for the Rosensweig system of ferrofluids ﻿

(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 ...