Applied Analysis
Browse by
Recent Submissions
-
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 ... -
Topological singular set of vector-valued maps, I: application to manifold-constrained Sobolev and BV spaces
(Calculus of Variations and Partial Differential Equations, 2019-03-30)We introduce an operator $\mathbf{S}$ on vector-valued maps $u$ which has the ability to capture the relevant topological information carried by $u$. In particular, this operator is defined on maps that take values in a ... -
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 ... -
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 ... -
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 ... -
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 ...
RSS 1.0