Now showing items 144-163 of 241

• On the Relationship between the One-Corner Problem and the $M-$Corner Problem for the Vortex Filament Equation ﻿

(2018-06-28)
In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular M-corner polygon as initial datum can be explained at infinitesimal times as the superposition of M one-corner initial ...
• On the Schrödinger map for regular helical polygons in the hyperbolic space ﻿

(2022-01-01)
The main purpose of this article is to understand the evolution of X t = X s ∧− X ss , with X(s, 0) a regular polygonal curve with a nonzero torsion in the three-dimensional Minkowski space. Unlike in the case of the ...
• On the smallness condition in linear inviscid damping: monotonicity and resonance chains ﻿

(2020)
We consider the effects of mixing by smooth bilipschitz shear flows in the linearized Euler equations on $\mathbb{T}_{L}\times\mathbb{R}$. Here, we construct a model which is closely related to a small high frequency ...
• On the unique continuation of solutions to non-local non-linear dispersive equations ﻿

(2020-08-02)
We prove unique continuation properties of solutions to a large class of nonlinear, non-local dispersive equations. The goal is to show that if (Formula presented.) are two suitable solutions of the equation defined in ...
• On the uniqueness of minimisers of Ginzburg-Landau functionals ﻿

(2020)
We provide necessary and sufficient conditions for the uniqueness of minimisers of the Ginzburg-Landau functional for Rn-valued maps under a suitable convexity assumption on the potential and for H1=2 \ L1 boundary data ...
• Optimal control of the Lotka–Volterra system: turnpike property and numerical simulations ﻿

(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 ...
• An optimal scaling to computationally tractable dimensionless models: Study of latex particles morphology formation ﻿

(2020-02)
In modelling of chemical, physical or biological systems it may occur that the coefficients, multiplying various terms in the equation of interest, differ greatly in magnitude, if a particular system of units is used. Such ...
• Order Reconstruction for neatics on squares with isotropic inclusions: A Landau-de Gennes study ﻿

(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 ﻿

(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 ...
• Pointwise Convergence of the Schr\"odinger Flow ﻿

(2021-01)
In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schr\"odinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain ...
• Pointwise Convergence over Fractals for Dispersive Equations with Homogeneous Symbol ﻿

(2021-08-24)
We study the problem of pointwise convergence for equations of the type $i\hbar\partial_tu + P(D)u = 0$, where the symbol $P$ is real, homogeneous and non-singular. We prove that for initial data $f\in H^s(\mathbb{R}^n)$ ...
• Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates ﻿

(2018-09)
We show that if $v\in A_\infty$ and $u\in A_1$, then there is a constant $c$ depending on the $A_1$ constant of $u$ and the $A_{\infty}$ constant of $v$ such that \Big\|\frac{ T(fv)} {v}\Big\|_{L^{1,\infty}(uv)}\le c\, ...
• A pseudospectral method for the one-dimensional fractional Laplacian on R ﻿

(2021-01-15)
In this paper, we propose a novel pseudospectral method to approximate accurately and efficiently the fractional Laplacian without using truncation. More precisely, given a bounded regular function defined over R, we map ...
• Pseudospectral Methods for the Fractional Laplacian on R ﻿

(2020-07-02)
In this thesis, first, we propose a novel pseudospectral method to approximate accu- rately and efficiently the fractional Laplacian without using truncation. More pre- cisely, given a bounded regular function defined over ...
• A quantitative approach to weighted Carleson condition ﻿

(2017-05-05)
Quantitative versions of weighted estimates obtained by F. Ruiz and J.L. Torrea for the operator $\mathcal{M}f(x,t)=\sup_{x\in Q,\,l(Q)\geq t}\frac{1}{|Q|}\int_{Q}|f(x)|dx \qquad x\in\mathbb{R}^{n}, \, t \geq0$ are ...
• Quantitative weighted estimates for rough homogeneous singular integrals ﻿

(2017-03-11)
We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space $L^2(w)$, we obtain a bound ...
• Quantitative weighted estimates for Rubio de Francia's Littlewood--Paley square function ﻿

(2019-12)
We consider the Rubio de Francia's Littlewood--Paley square function associated with an arbitrary family of intervals in $\mathbb{R}$ with finite overlapping. Quantitative weighted estimates are obtained for this operator. ...
• Quantitative weighted estimates for singular integrals and commutators ﻿

(2018-02-27)
In this dissertation several quantitative weighted estimates for singular integral op- erators, commutators and some vector valued extensions are obtained. In particular strong and weak type $(p, p)$ estimates, Coifman-Fe ...
• Quantitative weighted mixed weak-type inequalities for classical operators ﻿

(2016-06-30)
We improve on several mixed weak type inequalities both for the Hardy-Littlewood maximal function and for Calderón-Zygmund operators. These type of inequalities were considered by Muckenhoupt and Wheeden and later on by ...
• Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS ﻿

(2022-01-01)
The periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasi-invariance of the Gaussian measure on L2(T) with covariance [1+(−Δ)s]−1 ...