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Now showing items 1-10 of 10

#### On the improvement of the Hardy inequality due to singular magnetic fields

(2020-09-01)

We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type ...

#### 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 ...

#### Riemann's non-differentiable function and the binormal curvature flow

(2020-07-14)

We make a connection between a famous analytical object introduced in the 1860s by Riemann, as well as some variants of it, and a nonlinear geometric PDE, the binormal curvature flow. As a consequence this analytical object ...

#### Vortex Filament Equation for a regular polygon in the hyperbolic plane

(2020-07-09)

The aim of this article is twofold. First, we show the evolution of the vortex filament equation (VFE) for a regular planar polygon in the hyperbolic space. Unlike in the Euclidean space, the planar polygon is open and ...

#### On the energy of critical solutions of the binormal flow

(2020-07-02)

The binormal flow is a model for the dynamics of a vortex filament in a 3-D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1-D cubic ...

#### Evolution of Polygonal Lines by the Binormal Flow

(2020-06-01)

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schrödinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. Finally ...

#### Asymptotics in Fourier space of self-similar solutions to the modified Korteweg-de Vries equation

(2020-05-01)

We give the asymptotics of the Fourier transform of self-similar solutions for the modified Korteweg-de Vries equation. In the defocussing case, the self-similar profiles are solutions to the Painlevé II equation; although ...

#### Uniqueness properties of solutions to the Benjamin-Ono equation and related models

(2020-03-15)

We prove that if u1,u2 are real solutions of the Benjamin-Ono equation defined in (x,t)∈R×[0,T] which agree in an open set Ω⊂R×[0,T], then u1≡u2. We extend this uniqueness result to a general class of equations of Benjamin-Ono ...

#### Evolution of Polygonal Lines by the Binormal Flow

(2020-02-05)

The aim of this paper is threefold. First we display solutions of the cubic nonlinear Schr ̈odinger equation on R in link with initial data a sum of Dirac masses. Secondly we show a Talbot effect for the same equation. ...

#### A Hardy-type inequality and some spectral characterizations for the Dirac–Coulomb operator

(2020-01-01)

We prove a sharp Hardy-type inequality for the Dirac operator. We exploit this inequality to obtain spectral properties of the Dirac operator perturbed with Hermitian matrix-valued potentials V of Coulomb type: we characterise ...