Linear and NonLinear Waves
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ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2
(2022)We revisit a result from “Pointwise convergence of the Schr ̈odinger flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research Notices, 2021 (1), 596647” regarding the pointwise convergence of ... 
Lifespan estimates for the compressible Euler equations with damping via Orlicz spaces techniques
(20231006)In this paper we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time dependent damping and small initial perturbations. We employ some techniques from the blowup study ... 
Eigenvalue Curves for Generalized MIT Bag Models
(2021)We study spectral properties of Dirac operators on bounded domains Ω ⊂ R 3 with boundary conditions of electrostatic and Lorentz scalar type and which depend on a parameter τ ∈ R; the case τ = 0 corresponds to the MIT ... 
On the existence of weak solutions for the 2D incompressible Euler equations with inout flow and source and sink points
(2021)Wellposedness for the two dimensional Euler system with given initial vorticity is known since the works of Judoviˇc. In this paper we show existence of solutions in the case where we allowed the fluid to enter in and ... 
Unbounded growth of the energy density associated to the Schrödinger map and the binormal flow
(2021)We consider the binormal flow equation, which is a model for the dynamics of vortex filaments in Euler equations. Geometrically it is a flow of curves in three dimensions, explicitly connected to the 1D Schr¨odinger map ... 
On the one dimensional cubic NLS in a critical space
(2021)In this note we study the initial value problem in a critical space for the one dimensional Schr¨odinger equation with a cubic nonlinearity and under some smallness conditions. In particular the initial data is given by ... 
On the Calderón problem for nonlocal Schrödinger equations with homogeneous, directionally antilocal principal symbols
(20221225)In this article we consider direct and inverse problems for αstable, elliptic nonlocal operators whose kernels are possibly only supported on cones and which satisfy the structural condition of directional antilocality ... 
Sharp local smoothing estimates for Fourier integral operators
(2019)The theory of Fourier integral operators is surveyed, with an emphasis on local smoothing estimates and their applications. After reviewing the classical background, we describe some recent work of the authors which ... 
ENERGY CONSERVATION FOR 2D EULER WITH VORTICITY IN L(log L)α*
(20220101)In these notes we discuss the conservation of the energy for weak solutions of the twodimensional incompressible Euler equations. Weak solutions with vorticity in (Formula presented) with p > 3/2 are always conservative, ... 
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 ... 
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 ... 
Discrepancy of Minimal Riesz Energy Points
(20211201)We find upper bounds for the spherical cap discrepancy of the set of minimizers of the Riesz senergy on the sphere Sd. Our results are based on bounds for a Sobolev discrepancy introduced by Thomas Wolff in an unpublished ... 
Selfadjointness of twodimensional Dirac operators on corner domains
(20210101)We investigate the selfadjointness of the twodimensional Dirac operator D, with quantumdot and Lorentzscalar ishell boundary conditions, on piecewise C2 domains (with finitely many corners). For both models, we prove ... 
Dirac Operators and Shell Interactions: A Survey
(20210101)In this survey we gather recent results on Dirac operators coupled with δshell interactions. We start by discussing recent advances regarding the question of selfadjointness for these operators. Afterwards we switch to ... 
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 ... 
The Frisch–Parisi formalism for fluctuations of the Schrödinger equation
(2022)We consider the solution of the Schrödinger equation $u$ in $\mathbb{R}$ when the initial datum tends to the Dirac comb. Let $h_{\text{p}, \delta}(t)$ be the fluctuations in time of $\int\lvert x \rvert^{2\delta}\lvert ... 
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 ... 
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 ... 
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 ... 
Numerical approximation of the fractional Laplacian on R using orthogonal families
(20201201)In this paper, using wellknown complex variable techniques, we compute explicitly, in terms of the F12 Gaussian hypergeometric function, the onedimensional fractional Laplacian of the complex Higgins functions, the complex ...