## Section: New Results

### 1D quintic nonlinear equation with white noise dispersion

Participant : Arnaud Debussche.

Under certain scaling the nonlinear Schrödinger equation with random dispersion converges to the nonlinear Schrödinger equation with white noise dispersion. The aim of these works is to prove that this latter equation is globally well posed in ${L}^{2}$ or ${H}^{1}$. In [28] , we improve the Strichartz estimates obtained previously for the Schrödinger equation with white noise dispersion in one dimension. This allows us to prove global well posedness when a quintic critical nonlinearity is added to the equation. We finally show that the white noise dispersion is the limit of smooth random dispersion