Applied Analysis
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A Global wellposedness result for the Rosensweig system of ferrofluids
(Rev. Mat. Iberoam., 2019)In this Paper we study a BlochTorrey regularization of the Rosensweig system for ferrofluids. The scope of this paper is twofold. First of all, we investigate the existence and uniqueness of LerayHopf solutions of this ... 
Uniqueness of degreeone Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7
(Comptes Rendus Mathematique, 20180901)For ε>0, we consider the GinzburgLandau functional for RNvalued 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 BerisEdwards model of nematic liquid crystals
(Proceedings of the Royal Society AMathematical, Physical and Engineering Sciences, 20180214)We consider the BerisEdwards 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 BerisEdwards system modeling nematic liquid crystals
(Archive for Rational Mechanics and Analysis, 20180810)We consider the BerisEdwards system modelling incompressible liquid crystal flows of nematic type. This couples a NavierStokes system for the fluid velocity with a parabolic reactionconvectiondiffusion equation for the ... 
Some remark on the existence of infinitely many nonphysical solutions to the incompressible NavierStokes equations
(Journal of Mathematical Analysis and Applications, 201810)We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible NavierStokes equations in $ \mathbb{R}^2 $ and Burgers equation in $\mathbb{R} $ with vanishing ... 
On the global wellposedness of a class of 2D solutions for the Rosensweig system of ferrofluids
(Journal of Differential Equations, 201809)We study a class of 2D solutions of a BlochTorrey 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 Gammaconvergence discretetocontinuum approach
(Archive for Rational Mechanics and Analysis, 201807)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 nontrivial interplay between the topology of the shell and the alignment ... 
Zero limit of entropic relaxation time for the Shliomis model of ferrofluids
(20180211)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, 201711)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 ... 
Spherevalued harmonic maps with surface energy and the K13 problem
(Advances in the Calculus of Variations, 201711)We consider an energy functional motivated by the celebrated K13 problem in the OseenFrank theory of nematic liquid crystals. It is defined for spherevalued functions and appears as the usual Dirichlet energy with an ... 
Global wellposedness and twistwave solutions for the inertial QianSheng model of liquid crystals
(Journal of Differential Equations, 20171002)We consider the inertial QianSheng model of liquid crystals which couples a hyperbolictype equation involving a secondorder material derivative with a forced incompressible NavierStokes system. We study the energy law ... 
Dispersive effects of weakly compressible and fast rotating inviscid fluids
(Discrete and Continuous Dynamical Systems  Series A, 201708)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, 201707)We prove that the threedimensional, 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, 20170715)We consider a system describing the dynamics of an hydrodynamical, densitydependent 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 topologypreserving approximations of rough domains
(Calculus of Variations and Partial Differential Equations, 20170101)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 oneconstant approximation
(Mathematical Models and Methods in Applied Sciences, 20161231)We consider the twodimensional Landaude 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
(20161214)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 nonlocal terms and singular potentials
(20161212)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, 20160901)The LotkaVolterra 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 ...