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

  de la Hoz, F.; Kumar, S.; Vega, L. (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 ...

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

  Banica, V.; Vega, L. (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 ...

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

  Cassano, B.; Pizzichillo, F.; Vega, L. (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 ...

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

  Kenig, C. E.; Ponce, G.; Vega, L. (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 ...

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

  Correia, S.; Côte, R.; Vega, L. (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 ...

• Evolution of Polygonal Lines by the Binormal Flow 

  Banica, V.; Vega, L. (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 ...

• On the energy of critical solutions of the binormal flow 

  Banica, V.; Vega, L. (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 ...

• On the unique continuation of solutions to non-local non-linear dispersive equations 

  Kenig, C. E.; Pilod, D.; Ponce, G.; Vega, L. (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 improvement of the Hardy inequality due to singular magnetic fields 

  Fanelli, L.; Krejčiřík, D.; Laptev, A.; Vega, L. (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 ...

• Echo Chains as a Linear Mechanism: Norm Inflation, Modified Exponents and Asymptotics 

  Deng, Y.; Zillinger, C. (2021-07-30)

  In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to ...

• Static and Dynamical, Fractional Uncertainty Principles 

  Kumar, S.; Ponce-Vanegas, F.; Vega, L. (2021-03)

  We study the process of dispersion of low-regularity solutions to the Schrödinger equation using fractional weights (observables). We give another proof of the uncertainty principle for fractional weights and use it to get ...

• Invariant measures for the dnls equation 

  Lucà, R. (2020-10-02)

  We describe invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schr\"odinger equation (DNLS) constructed in \cite{MR3518561, Genovese2018}. The construction works for small $L^2$ ...

• Magnetic domain-twin boundary interactions in Ni-Mn-Ga 

  Veligatla, M.; Garcia-Cervera, C.J.; Müllner, P. (2020-04)

  The stress required for the propagation of twin boundaries in a sample with fine twins increases monotonically with ongoing deformation. In contrast, for samples with a single twin boundary, the stress exhibits a plateau ...

• Sensitivity of twin boundary movement to sample orientation and magnetic field direction in Ni-Mn-Ga 

  Veligatla, M.; Titsch, C.; Drossel, W.-G.; Garcia-Cervera, C.J.; Müllner, P. (2019)

  When applying a magnetic field parallel or perpendicular to the long edge of a parallelepiped Ni- Mn-Ga stick, twin boundaries move instantaneously or gradullay through the sample. We evaluate the sample shape dependence ...

• A sharp lorentz-invariant strichartz norm expansion for the cubic wave equation in \mathbb{R}^{1+3} 

  Negro, G. (2020)

  We provide an asymptotic formula for the maximal Stri- chartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi’s sharp constant for the linear Strichartz ...

• Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory 

  Del Teso, F.; Endal, J.; R. Jakobsen, E. (2019)

  Abstract. We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations ∂tu − Lσ,μ[φ(u)] = f(x,t) in RN × (0,T), where Lσ,μ is a general ...

• Bayesian approach to inverse scattering with topological priors 

  Carpio, A.; Iakunin, S.; Stadler, G. (2020)

  We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite ...

• The Schrödinger equation and Uncertainty Principles 

  Aguirre, M. (2020-09)

  The main task of this thesis is the analysis of the initial data u0 of Schrödinger’s initial value problem in order to determine certain properties of its dynamical evolution. First we consider the elliptic Schrödinger ...

• On the smallness condition in linear inviscid damping: monotonicity and resonance chains 

  Deng, Y.; Zillinger, C. (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 ...

• A geometric and physical study of Riemann's non-differentiable function 

  Eceizabarrena, D. (2020-07-08)

  Riemann's non-differentiable function is a classic example of a continuous but almost nowhere differentiable function, whose analytic regularity has been widely studied since it was proposed in the second half of the 19th ...

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