• El efecto de Talbot: de la óptica a la ecuación de Schrödinger 

  Eceizabarrena D. (TEMat, 2017-07)

  El objetivo de este artículo es dar a conocer un bello efecto óptico que se denomina efecto de Talbot. Primero, describiremos el fenómeno y comentaremos su descubrimiento a mediados del siglo XIX. A continuación, analizaremos ...

• Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments 

  del Teso F.; Endal J.; Jakobsen E.R. (SIAM Journal on Numerical Analysis, 2018)

  \noindent We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations $$ \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad ...

• Uniqueness of degree-one Ginzburg–Landau vortex in the unit ball in dimensions N ≥ 7 

  Ignat R.; Nguyen L.; Slastikov V.; Zarnescu A. (Comptes Rendus Mathematique, 2018-09-01)

  For ε>0, we consider the Ginzburg-Landau functional for RN-valued maps defined in the unit ball BN⊂RN with the vortex boundary data x on ∂BN. In dimensions N≥7, we prove that for every ε>0, there exists a unique global ...

• Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals 

  Murza A.C.; Teruel A.E.; Zarnescu A. (Proceedings of the Royal Society A-Mathematical, Physical and Engineering Sciences, 2018-02-14)

  We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in ...

• Dynamics and flow effects in the Beris-Edwards system modeling nematic liquid crystals 

  Hao W; Xiang X; Zarnescu A (Archive for Rational Mechanics and Analysis, 2018-08-10)

  We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion equation for the ...

• Some remark on the existence of infinitely many nonphysical solutions to the incompressible Navier-Stokes equations 

  Scrobogna S. (Journal of Mathematical Analysis and Applications, 2018-10)

  We prove that there exist infinitely many distributional solutions with infinite kinetic energy to both the incompressible Navier-Stokes equations in $ \mathbb{R}^2 $ and Burgers equation in $\mathbb{R} $ with vanishing ...

• Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates 

  Li K.; Ombrosi S.; Pérez C. (Mathematische Annalen, 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\, ...

• On the global well-posedness of a class of 2D solutions for the Rosensweig system of ferrofluids 

  Scrobogna S. (Journal of Differential Equations, 2018-09)

  We study a class of 2D solutions of a Bloch-Torrey regularization of the Rosensweig system in the whole space, which arise when the initial data and the external magnetic field are 2D. We prove that such solutions are ...

• Weighted norm inequalities for rough singular integral operators 

  Li K.; Pérez C.; Rivera-Ríos I.; Roncal L. (Journal of Geometric Analysis, 2018-08-17)

  In this paper we provide weighted estimates for rough operators, including rough homogeneous singular integrals $T_\Omega$ with $\Omega\in L^\infty(\mathbb{S}^{n-1})$ and the Bochner--Riesz multiplier at the critical index ...

• Defects in Nematic Shells: a Gamma-convergence discrete-to-continuum approach 

  Canevari G.; Segatti A. (Archive for Rational Mechanics and Analysis, 2018-07)

  In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a non-trivial interplay between the topology of the shell and the alignment ...

• On the regularity of solutions to the k-generalized korteweg-de vries equation 

  Kenig C.E.; Linares F.; Ponce G.; Vega L. (Proceedings of the American Mathematical Society, 2018-07)

  This work is concerned with special regularity properties of solutions to the k-generalized Korteweg-de Vries equation. In [Comm. Partial Differential Equations 40 (2015), 1336–1364] it was established that if the initial ...

• Absence of eigenvalues of two-dimensional magnetic Schroedinger operators 

  Fanelli L.; Krejcirik D.; Vega L. (2018-01-01)

  By developing the method of multipliers, we establish sufficient conditions on the electric potential and magnetic field which guarantee that the corresponding two-dimensional Schroedinger operator possesses no point ...

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

  Correia S.; Côte R.; Vega L. (2018-07-06)

  We give the asymptotics of the Fourier transform of self-similar solutions to the modified Korteweg-de Vries equation, through a fixed point argument in weighted $W^{1,\infty}$ around a carefully chosen, two term ansatz. ...

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

  Fanelli L.; Krejcirik D.; Laptev A.; Vega L. (2018-07-12)

  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 ...

• Regularity of fractional maximal functions through Fourier multipliers 

  Beltran D.; Ramos J. P.; Saari O. (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 ...

• Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds 

  Beltran D.; Hickman J.; Sogge C. D. (2018)

  The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian ...

• Sparse bounds for pseudodifferential operators 

  Beltran D.; Cladek L. (Journal d'Analyse Mathématique, 2018)

  We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of ...

• Spectral stability of Schrödinger operators with subordinated complex potentials 

  Fanelli L.; Krejcirik D.; Vega L. (Journal of Spectral Theory, 2018-06-28)

  We prove that the spectrum of Schroedinger operators in three dimensions is purely continuous and coincides with the non-negative semiaxis for all potentials satisfying a form-subordinate smallness condition. By developing ...

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

  De la Hoz F.; Vega L. (Journal of Nonlinear Science, 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 ...

• Sharp exponential localization for eigenfunctions of the Dirac Operator 

  Cassano B. (2018)

  We determine the fastest possible rate of exponential decay at infinity for eigenfunctions of the Dirac operator $\mathcal D_n + \mathbb V$, being $\mathcal D_n$ the massless Dirac operator in dimensions $n=2,3$ and ...

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