Browsing Applied Analysis by Title
Now showing items 1-20 of 25
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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 ...