Browsing Linear and NonLinear Waves by Title
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On the bound states of Schrödinger operators with $\delta$interactions on conical surfaces
(20160630)In dimension greater than or equal to three, we investigate the spectrum of a Schrödinger operator with a $\delta$interaction supported on a cone whose cross section is the sphere of codimension two. After decomposing ... 
On the energy of critical solutions of the binormal flow
(20190720)The binormal flow is a model for the dynamics of a vortex filament in a 3D inviscid incompressible fluid. The flow is also related with the classical continuous Heisen berg model in ferromagnetism, and the 1D cubic Schr ... 
On the energy of critical solutions of the binormal flow
(20200702)The binormal flow is a model for the dynamics of a vortex filament in a 3D inviscid incompressible fluid. The flow is also related with the classical continuous Heisenberg model in ferromagnetism, and the 1D cubic ... 
On the Evolution of the Vortex Filament Equation for regular Mpolygons with nonzero torsion
(20190903)In this paper, we consider the evolution of the Vortex Filament equa tion (VFE): Xt = Xs ∧ Xss, taking Msided regular polygons with nonzero torsion as initial data. Us ing algebraic techniques, backed by numerical ... 
On the Hausdorff dimension of Riemann's nondifferentiable function
(20210101)Recent findings show that the classical Riemann's nondifferentiable function has a physical and geometric nature as the irregular trajectory of a polygonal vortex filament driven by the binormal flow. In this article, we ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20180712)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20180712)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the improvement of the Hardy inequality due to singular magnetic fields
(20200901)We establish magnetic improvements upon the classical Hardy inequality for two specific choices of singular magnetic fields. First, we consider the AharonovBohm field in all dimensions and establish a sharp Hardytype ... 
On the regularity of solutions to the kgeneralized kortewegde vries equation
(201807)This work is concerned with special regularity properties of solutions to the kgeneralized Kortewegde Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ... 
On the regularity of solutions to the kgeneralized kortewegde vries equation
(20180101)This work is concerned with special regularity properties of solutions to the kgeneralized Kortewegde Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ... 
On the Relationship between the OneCorner Problem and the $M$Corner Problem for the Vortex Filament Equation
(20180628)In this paper, we give evidence that the evolution of the vortex filament equation (VFE) for a regular Mcorner polygon as initial datum can be explained at infinitesimal times as the superposition of M onecorner initial ... 
On the Schrödinger map for regular helical polygons in the hyperbolic space
(20220101)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 threedimensional 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 nonlocal nonlinear dispersive equations
(20200802)We prove unique continuation properties of solutions to a large class of nonlinear, nonlocal dispersive equations. The goal is to show that if (Formula presented.) are two suitable solutions of the equation defined in ... 
Pointwise Convergence of the Schr\"odinger Flow
(202101)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 ... 
A pseudospectral method for the onedimensional fractional Laplacian on R
(20210115)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
(20200702)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 ... 
Quasiinvariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS
(20220101)The periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasiinvariance of the Gaussian measure on L2(T) with covariance [1+(−Δ)s]−1 ... 
Reconstruction from boundary measurements for less regular conductivities
(20161001)In this paper, following Nachman's idea [14] and Haberman and Tataru's idea [9], we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $\nabla log\gamma$ in a Lipschitz ... 
Regularity of fractional maximal functions through Fourier multipliers
(2018)We prove endpoint bounds for derivatives of fractional maximal functions with either smooth convolution kernel or lacunary set of radii in dimensions $n \geq 2$. We also show that the spherical fractional maximal function ...