One-day workshop on

Probabilistic aspects of nonlinear dispersive equations

 

 

 

The 2d nonlinear Schrödinger equation with a white noise potential

 

Nikolay Tzvetkov

 

Using an approach introduced by Hairer-Labbe we construct a unique global dynamics for the NLS on T^2 with a white noise potential and an arbitrary polynomial nonlinearity. We build the solutions as a limit of classical solutions (up to a phase shift) of the same equation with smoothed potentials. This is an extension of previous contributions by Debussche-Weber dealing with a cubic nonlinearity.