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math.AP2026
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 resul…
math.AP2025
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 mea…
math.AP2024
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…