### Recent Submissions

• #### On a hyperbolic system arising in liquid crystal modelling ﻿

(Journal of Hyperbolic Differential Equations, 2017-11)
We consider a model of liquid crystals, based on a nonlinear hyperbolic system of differential equations, that represents an inviscid version of the model proposed by Qian and Sheng. A new concept of dissipative solution ...
• #### Sphere-valued harmonic maps with surface energy and the K13 problem ﻿

(Advances in the Calculus of Variations, 2017-11)
We consider an energy functional motivated by the celebrated K13 problem in the Oseen-Frank theory of nematic liquid crystals. It is defined for sphere-valued functions and appears as the usual Dirichlet energy with an ...
• #### Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals ﻿

(Journal of Differential Equations, 2017-10-02)
We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law ...
• #### Klein's Paradox and the Relativistic $\delta$-shell Interaction in $\mathbb{R}^3$ ﻿

(Analysis & PDE, 2017-11)
Under certain hypothesis of smallness of the regular potential $\mathbf{V}$, we prove that the Dirac operator in $\mathbb{R}^3$ coupled with a suitable re-scaling of $\mathbf{V}$, converges in the strong resolvent sense ...
• #### Asymptotic behaviour for fractional diffusion-convection equations ﻿

(2017-10)
We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ...
• #### Existence of weak solutions for a general porous medium equation with nonlocal pressure ﻿

(submitted, 2017-10)
We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ...
• #### Three-dimensional coarsening dynamics of a conserved, nematic liquid crystal-isotropic fluid mixture ﻿

(Journal of Non-Newtonian Fluid Mechanics, 2017-09)
We present a numerical investigation of the three-dimensional coarsening dynamics of a nematic liquid crystal-isotropic fluid mixture using a conserved phase field model. The model is a coupled system for a generalized ...
• #### SPECTRAL ASYMPTOTICS FOR $\delta$-INTERACTIONS ON SHARP CONES ﻿

(Journal of Mathematical Analysis and Applications, 2017)
We investigate the spectrum of three-dimensional Schr\"odinger operators with $\delta$-interactions of constant strength supported on circular cones. As shown in earlier works, such operators have infinitely many eigenvalues ...
• #### Weighted mixed weak-type inequalities for multilinear operators ﻿

(Studia Mathematica, 2017)
In this paper we present a theorem that generalizes Sawyer's classic result about mixed weighted inequalities to the multilinear context. Let $\vec{w}=(w_1,...,w_m)$ and $\nu = w_1^\frac{1}{m}...w_m^\frac{1}{m}$, the main ...
• #### Mixed norm estimates for the Cesàro means associated with Dunkl-Hermite expansions ﻿

(Transactions of the American Mathematical Society, 2017)
Our main goal in this article is to study mixed norm estimates for the Cesàro means associated with Dunkl--Hermite expansions on $\mathbb{R}^d$. These expansions arise when one considers the Dunkl--Hermite operator ...
• #### Dispersive effects of weakly compressible and fast rotating inviscid fluids ﻿

(Discrete and Continuous Dynamical Systems - Series A, 2017-08)
We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $H^s \left( \mathbb{R}^3 \right), s>5/2$. ...

We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p} ... • #### The relativistic spherical$\delta$-shell interaction in$\mathbb{R}^3$: spectrum and approximation ﻿ (Journal of Mathematical Physics, 2017-08-03) This note revolves on the free Dirac operator in$\mathbb{R}^3$and its$\delta$-shell interaction with electrostatic potentials supported on a sphere. On one hand, we characterize the eigenstates of those couplings by ... • #### Highly rotating fluids with vertical stratification for periodic data and vanishing vertical viscosity ﻿ (Revista Matemática Iberoamericana, 2017-07) We prove that the three-dimensional, periodic primitive equations with zero vertical diffusivity are globally well posed if the Rossby and Froude number are sufficiently small. The initial data is considered to be of zero ... • #### Sharp weighted estimates involving one supremum ﻿ (Comptes Rendus Mathematique, 2017-07) In this note, we study the sharp weighted estimate involving one supremum. In particular, we give a positive answer to an open question raised by Lerner and Moen. We also extend the result to rough homogeneous singular ... • #### Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system ﻿ (Discrete and Continuous Dynamical Systems - Series A, 2017-07-15) We consider a system describing the dynamics of an hydrodynamical, density-dependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ... • #### Monotonicity and convexity of the ratios of the first kind modified Bessel functions and applications ﻿ (Mathematical Inequalities & Applications, 2017-07-18) Let$I_{v}\left( x\right) $be modified Bessel functions of the first kind. We prove the monotonicity property of the function$x\mapsto I_{u}\left( x\right) I_{v}\left( x\right) /I_{\left( u+v\right) /2}\left( x\right) ...
Let $I_{\nu }\left( x\right)$ be the modified Bessel functions of the first kind of order $\nu$, and $S_{p,\nu }\left( x\right) =W_{\nu }\left( x\right) ^{2}-2pW_{\nu }\left( x\right) -x^{2}$ with \$W_{\nu }\left( x\right) ...