Applied Analysis
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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 ... -
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 ... -
Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
(Comptes Rendus Mathematique, 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 ... -
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 ... -
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 ... -
Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations
(Journal of Mathematical Analysis and Applications, 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 ... -
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 ... -
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 ... -
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. -
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 ... -
Sphere-valued harmonic maps with surface energy and the K13 problem
(Advances in the Calculus of Variations, 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 ... -
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 ... -
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 $. ... -
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 ... -
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 ... -
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 ... -
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 ... -
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 ... -
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, ... -
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 ...
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