Visciglia: On the Nonlinear Schroedinger Equation with multiplicative white noise

Visciglia: 
We prove global existence, uniqueness and convergence almost surely of solutions to a family of properly regularized and renormalized approximating equations to the Nonlinear Schroedinger Equation. One of the difficulties is connected with the low regularity of the white noise potential, that does not allow the use of the standard definition of product between functions.We show how this problem can be settled by using a suitable renormalization argument, once we exploit a transformation first introduced by Hairer in the context of the heat equation. Next we show how the use of suitable energies allow to extend the solutions for every time almost surely w.r.t. to the probabilistic parameter defining the white noise potential.
In particular we extend a previous result by A. Debussche and H. Weber available in the case of a cubic Nonlinearity.
This is a joint work with N. Tzvetkov.
http://cvgmt.sns.it/seminar/815/

When	Fri Jun 4, 2021 2:30pm – 3:30pm Coordinated Universal Time
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