most citedProbabilistic global well-posedness for the supercritical nonlinear harmonic oscillator

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math.AP2023

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.…

math.AP2013★ 20 cited

Probabilistic global well-posedness for the supercritical nonlinear harmonic oscillator

Aurélien Poiret, Didier Robert, Laurent Thomann

Thanks to an approach inspired from Burq-Lebeau \cite{bule}, we prove stochastic versions of Strichartz estimates for Schrödinger with harmonic potential. As a consequence, we show…

math.AP2013

Random weighted Sobolev inequalities on and application to Hermite functions

Aurélien Poiret, Didier Robert, Laurent Thomann

We extend a randomisation method, introduced by Shiffman-Zelditch and developed by Burq-Lebeau on compact manifolds for the Laplace operator, to the case of with the…