43 citations · 108 across the 17 of their papers we have counts for
25 papers
Blow-up for the 1D cubic NLS
Valeria Banica, Renato Lucà, Nikolay Tzvetkov +1
We consider the 1D cubic NLS on and prove a blow-up result for functions that are of borderline regularity, i.e. for any for the Sobolev scale and $…
Magnetic Reconnection in Magnetohydrodynamics
Pedro Caro, Gennaro Ciampa, Renato Lucà
We provide examples of periodic solutions (in both 2 and 3 dimension) of the Magnetohydrodynamics equations such that the topology of the magnetic lines changes during the evolutio…
Quasi-invariance of Gaussian measures for the periodic Benjamin-Ono-BBM equation
Giuseppe Genovese, Renato Lucá, Nikolay Tzvetkov
The BBM equation is a Hamiltonian PDE which revealed to be a very interesting test-model to study the transformation property of Gaussian measures along the flow. In this paper we…
Transport of Gaussian measures with exponential cut-off for Hamiltonian PDEs
Giuseppe Genovese, Renato Lucà, Nikolay Tzvetkov
We show that introducing an exponential cut-off on a suitable Sobolev norm facilitates the proof of quasi-invariance of Gaussian measures with respect to Hamiltonian PDE flows and…
Convergence over fractals for the Schrödinger equation
Renato Lucà, Felipe Ponce-Vanegas
We consider a fractal refinement of the Carleson problem for the Schrödinger equation, that is to identify the minimal regularity needed by the solutions to converge pointwise to t…
Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS
Giuseppe Genovese, Renato Lucà, Nikolay Tzvetkov
The periodic DNLS gauge is an anticipative map with singular generator which revealed crucial in the study of the periodic derivative NLS. We prove quasi-invariance of the Gaussian…
Convergence over fractals for the periodic Schrödinger equation
Daniel Eceizabarrena, Renato Lucà
We consider a fractal refinement of Carleson's problem for pointwise convergence of solutions to the periodic Schrödinger equation to their initial datum. For and \[ s…
Pointwise Convergence of the Schrödinger Flow
E. Compaan, R. Lucà, G. Staffilani
In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schrödinger flows to the initial data, in both the continuous and the periodic settings.…
Invariant measures for the periodic derivative nonlinear Schrödinger equation
Giuseppe Genovese, Renato Lucà, Daniele Valeri
We construct invariant measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation (DNLS) for small data in and we show these mea…
Polynomial mixing under a certain stationary Euler flow
Gianluca Crippa, Renato Lucà, Christian Schulze
We study the mixing properties of a scalar advected by a certain incompressible velocity field on the two dimensional unit ball, which is a stationary radial solution of th…
A note on pointwise convergence for the Schrödinger equation
Renato Lucà, Keith Rogers
We consider Carleson's problem regarding pointwise convergence for the Schrödinger equation. Bourgain recently proved that there is initial data, in with $s<\fr…
A limiting absorption principle for the Helmholtz equation with variable coefficients
Federico Cacciafesta, Piero D'Ancona, Renato Lucà
We prove a limiting absorption principle for a generalized Helmholtz equation on an exterior domain with Dirichlet boundary conditions \begin{equation*} (L+λ)v=f, \qquad λ\in \math…
Vortex reconnection in the three dimensional Navier-Stokes equations
Alberto Enciso, Renato Luca, Daniel Peralta-Salas
We prove that the vortex structures of solutions to the 3D Navier-Stokes equations can change their topology without any loss of regularity. More precisely, we construct smooth hig…
Local Central Limit Theorem for a Random Walk Perturbed in One Point
Giuseppe Genovese, Renato Lucà
We consider a symmetric random walk on the -dimensional lattice, whose exit probability from the origin is modified by an antisymmetric perturbation and prove the local central…
Stability properties of the regular set for the Navier--Stokes equation
Renato Lucà, Piero D'Ancona
We investigate the size of the regular set for small perturbations of some classes of strong large solutions to the Navier--Stokes equation. We consider perturbations of the data w…
Singular integrals with angular integrability
Federico Cacciafesta, Renato Lucà
In this note we prove a class of sharp inequalities for singular integral operators in weighted Lebesgue spaces with angular integrability.
An improved necessary condition for the Schrödinger maximal estimate
Renato Lucà, Keith Rogers
We improve the necessary condition for Carleson's problem regarding convergence for the Schrödinger equation in dimensions . We prove that if the solution converges almost…
Average decay of the Fourier transform of measures with applications
Renato Lucà, Keith Rogers
We consider spherical averages of the Fourier transform of fractal measures and improve both the upper and lower bounds on the rate of decay. Maximal estimates with respect to frac…
Gibbs measures associated to the integrals of motion of the periodic derivative nonlinear Schrödinger equation
Giuseppe Genovese, Renato Lucà, Daniele Valeri
We study the one dimensional periodic derivative nonlinear Schrödinger (DNLS) equation. This is known to be a completely integrable system, in the sense that there is an infinite s…
On the regularity set and angular integrability for the Navier--Stokes equation
Piero D'Ancona, Renato Lucà
We investigate the size of the regular set for suitable weak solutions of the Navier--Stokes equation, in the sense of Caffarelli--Kohn--Nirenberg. We consider initial data in weig…
Helmholtz and dispersive equations with variable coefficients on exterior domains
Federico Cacciafesta, Piero D'Ancona, Renato Luca'
We prove smoothing estimates in Morrey-Campanato spaces for a Helmholtz equation with…
Regularity criteria with angular integrability for the Navier-Stokes equation
Renato Lucà
We give new a priori assumptions on weak solutions of the Navier-Stokes equation so as to be able to conclude that they are smooth. The regularity criteria are given in terms of mi…
Inequalities with angular integrability and applications
Renato Lucà
We prove an extension of the Stein-Weiss weighted estimates for fractional integrals, in the context of Lp spaces with different integrability properties in the radial and the angu…
Random Walk on Lattice with an Antisymmetric Perturbation in One Point
Giuseppe Genovese, Renato Lucà
We study an homogeneous irreducible markovian random walk in a square lattice of arbitrary dimension, with an antisymmetric perturbation acting only in one point. We compute exactl…