Renato Lucà

Ikerbasque Research Fellow

T +34 946 567 842
F +34 946 567 842

Information of interest

My research concerns harmonic analysis with applications to PDEs such as the Navier--Stokes, the Schrödinger and the wave equations.

  • Convergence over fractals for the Schrödinger equation 

    Lucà, R.Autoridad BCAM; Ponce Vanegas, F.Autoridad BCAM (2021-01)
    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 their initial data almost everywhere with ...
  • Pointwise Convergence of the Schr\"odinger Flow 

    Compaan, E.; Lucà, R.Autoridad BCAM; Staffilani, G. (2021-01)
    In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schr\"odinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain ...
  • Invariant measures for the dnls equation 

    Lucà, R.Autoridad BCAM (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 $L^2$ ...

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