Now showing items 84-103 of 119

• #### 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 ...
• #### Shell interactions for Dirac operators: On the point spectrum and the confinement ﻿

(SIAM Journal on Mathematical Analysis, 2015-12-31)
Spectral properties and the confinement phenomenon for the coupling $H + V$ are studied, where $H =-i\alpha \cdot \nabla + m\beta$ is the free Dirac operator in $\mathbb{R}^3$ and $V$ is a measure-valued potential. The ...
• #### Singular Perturbation of the Dirac Hamiltonian ﻿

(2017-12-15)
This thesis is devoted to the study of the Dirac Hamiltonian perturbed by delta-type potentials and Coulomb-type potentials. We analysed the delta-shell interaction on bounded and smooth domains and its approximation by ...
• #### Singularity formation for the 1-D cubic NLS and the Schrödinger map on $\mathbb{S}^2$ ﻿

(2017-02-02)
In this note we consider the 1-D cubic Schrödinger equation with data given as small perturbations of a Dirac-$\delta$ function and some other related equations. We first recall that although the problem for this type of ...
• #### 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 ...
• #### Some remarks on the $L^p$ regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition ﻿

(Rendiconti Lincei - Matematica e Applicazioni, 2017-05-30)
In this note we prove an end-point regularity result on the $L^P$ integrability of the second derivatives of solutions to non-divergence form uniformly elliptic equations whose second derivatives are a priori only known ...
• #### Sparse bounds for maximal rough singular integrals via the Fourier transform ﻿

(Annales de l'institut Fourier, 2019-03-12)
We prove a quantified sparse bound for the maximal truncations of convolution-type singular integrals with suitable Fourier decay of the kernel. Our result extends the sparse domination principle by Conde-Alonso, Culiuc, ...
• #### Sparse bounds for pseudodifferential operators ﻿

(Journal d'Analyse Mathématique, 2018)
We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of ...
• #### Sparse domination theorem for multilinear singular integral operators with $L^{r}$-Hörmander condition ﻿

(Michigan Mathematical Journal, 2017-04-01)
In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-Hörmander condition, then $T$ can be dominated by multilinear sparse operators.
• #### Spectral asymptotics for $\delta$-interactions on sharp cones ﻿

(Journal of Mathematical Analysis and Applications, 2017)
We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...
• #### Spectral asymptotics of the Dirichlet Laplacian in a conical layer ﻿

(Communications on Pure and Applied Analysis, 2015-05-01)
The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for ...
• #### Spectral stability of Schrödinger operators with subordinated complex potentials ﻿

(Journal of Spectral Theory, 2018-06-28)
We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing ...
• #### Spectral Transitions for Aharonov-Bohm Laplacians on Conical Layers ﻿

(2016-07-11)
We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary ...
• #### 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 ...
• #### A strategy for self-adjointness of Dirac operators: Applications to the MIT bag model and delta-shell interactions ﻿

(2016-12-21)
We develop an approach to prove self-adjointness of Dirac operators with boundary or transmission conditions at a $C^2$-compact surface without boundary. To do so we are lead to study the layer potential induced by the ...
• #### The dynamics of vortex filaments with corners ﻿

(Communications on Pure and Applied Analysis (CPAA), 2015-07-01)
This paper focuses on surveying some recent results obtained by the author together with V. Banica on the evolution of a vortex filament with one corner according to the so-called binormal flow. The case of a regular polygon ...
• #### The initial value problem for the binormal flow with rough data ﻿

(Annales Scientifiques de l'Ecole Normale Superieure, 2015-12-31)
In this article we consider the initial value problem of the binormal flow with initial data given by curves that are regular except at one point where they have a corner. We prove that under suitable conditions on the ...
• #### The Vortex Filament Equation as a Pseudorandom Generator ﻿

(Acta Applicandae Mathematicae, 2015-08-01)
In this paper, we consider the evolution of the so-called vortex filament equation (VFE), $$X_t = X_s \wedge X_{ss},$$ taking a planar regular polygon of M sides as initial datum. We study VFE from a completely novel ...
• #### Three Observations on Commutators of Singular Integral Operators with BMO Functions ﻿

(AWM-Springer Series, Harmonic Analysis, Partial Differentail Equations, Complex Analysis, Banach Spaces, and Operator Theory, 2016-07-01)
Three observations on commutators of Singular Integral Operators with BMO functions are exposed, namely 1 - The already known subgaussian local decay for the commutator, namely \$\[\frac{1}{|Q|}\left|\left\{x\in Q\, : ...
• #### Three-dimensional coarsening dynamics of a conserved, nematic liquid crystal-isotropic fluid mixture ﻿

(Journal of Non-Newtonian Fluid Mechanics, 2017-09)
We present a numerical investigation of the three-dimensional coarsening dynamics of a nematic liquid crystal-isotropic fluid mixture using a conserved phase field model. The model is a coupled system for a generalized ...