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+34 946 567 842
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+34 946 567 842
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rluca@bcamath.org
Information of interest
My research concerns harmonic analysis with applications to PDEs such as the Navier--Stokes, the Schrödinger and the wave equations.
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Quasi-invariance of low regularity Gaussian measures under the gauge map of the periodic derivative NLS
Genovese, G.; Lucà, R.
; Tzvetkov, N. (2022-01-01)
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 measure on L2(T) with covariance [1+(−Δ)s]−1 ...
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ALMOST SURE POINTWISE CONVERGENCE OF THE CUBIC NONLINEAR SCHRODINGER EQUATION ON ̈ T 2
Lucà, R. (2022)
We revisit a result from “Pointwise convergence of the Schr ̈odinger flow, E. Compaan, R. Luc`a, G. Staffilani, International Mathematics Research Notices, 2021 (1), 596-647” regarding the pointwise convergence of ...
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Convergence over fractals for the Schrödinger equation
Lucà, R.; Ponce Vanegas, F. (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 ...
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Pointwise Convergence of the Schr\"odinger Flow
Compaan, E.; Lucà, R.; 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 ...
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Invariant measures for the dnls equation
Lucà, R. (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 $L^2$ ...
