168 citations · 318 across the 32 of their papers we have counts for
35 papers
Gauge transforms, random averaging operator ansatz and improved probabilistic well-posedness for the radial NLS on the ball
Nicolas Burq, Nicolas Camps, Chenmin Sun +1
We construct probabilistic strong solutions to the cubic Schrödinger equation on the three-dimensional ball with radial initial data, which is a significant improvement of a result…
Almost surely smoothed scattering for cubic NLS
Nicolas Burq, Herbert Koch, Nicola Visciglia +1
We consider cubic NLS in dimensions 2, 3, 4 and we prove that almost surely solutions with randomized initial data at low regularity scatter. Moreover, we establish some smoothing…
The Second Picard iteration of NLS on the sphere does not regularize Gaussian random initial data
Nicolas Burq, Nicolas Camps, Mickaël Latocca +2
We consider the Wick ordered cubic Schrödinger equation (NLS) posed on the two-dimensional sphere, with initial data distributed according to a Gaussian measure. We show that the s…
Probabilistic well-posedeness for the nonlinear Schrödinger equation on the sphere I: positive regularities
Nicolas Burq, Nicolas Camps, Chenmin Sun +1
We establish the probabilistic well-posedness of the nonlinear Schrödinger equation on the sphere . The initial data are distributed according to Gaussian meas…
Semi-classical observation suffices for observability: wave and Schrödinger equations
Nicolas Burq, Belhassen Dehman, Jérôme Le Rousseau
For the wave and the Schrödinger equations we show how observability can be deduced from the observability of solutions localized in frequency according to a dyadic scale.
Bilinear Strichartz estimates and almost sure global solutions for the nonlinear Schr{ö}dinger equation
Nicolas Burq, Aurélien Poiret, Laurent Thomann
The purpose of this article is to construct global solutions, in a probabilistic sense, for the nonlinear Schr{ö}dinger equation posed on , in a supercritical regime.…