43 citations · 108 across the 17 of their papers we have counts for
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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…