114 citations · 322 across the 35 of their papers we have counts for
45 papers
On the parabolic model for the harmonic oscillator II: global existence and invariant measures
Aurélien Deya, Reika Fukuizumi, Laurent Thomann
We establish an a priori bound for the dynamical parabolic model with harmonic potential. This bound yields the global well-posedness of the equation and, via the Krylov-Bo…
On the parabolic model for the harmonic oscillator: diagrams and local existence
Aurélien Deya, Reika Fukuizumi, Laurent Thomann
We prove the local wellposedness of the (renormalized) parabolic model associated with the harmonic oscillator on , that is, the equation formally written as…
On the stability of the Abrikosov lattice in the Lowest Landau Level
Pierre Germain, Valentin Schwinte, Laurent Thomann
We study the Lowest Landau Level equation set on simply and doubly-periodic domains (in other words, rectangles and strips with appropriate boundary conditions). To begin with, we…
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.…
Renormalization of a 1d quadratic Schr{ö}dinger model with additive noise
Aurélien Deya, Reika Fukuizumi, Laurent Thomann
The study is devoted to the interpretation and wellposedness of the stochastic NLS model \begin{equation*} (\imath \partial_t-Δ)u=|u|^2+\dot{B}, \quad u_0=0,\quad \quad t\in \mathb…
Evolution of Gaussian measures and application to the one dimensional nonlinear Schr{ö}dinger equation
Laurent Thomann, Nicolas Burq
In this note, we give an overview of some results obtained in [3]. This latter work is devoted to the study of the one-dimensional nonlinear Schr{ö}dinger equation with random init…