Solving the 4NLS with White Noise Initial Data

Explore a lecture on solving the 4NLS (fourth-order nonlinear Schrödinger equation) with white noise initial data. Delve into the connection between white noise and partial differential equations, focusing on Hamiltonian PDEs. Examine the general globalization argument and its application to global solutions. Investigate the proof, limits, and complexity of the problem, including invariance properties and smooth solutions. Analyze the limit equation, compare more precise solutions, and study the Borg approach. Gain insights from speaker Nikolay Tzvetkov of the University of Cergy-Pontoise, France, in this comprehensive talk from the School and Workshop on Mixing and Control.

Intro
White Noise
Connection to PDE
Hamiltonian PDE
General Globalization Argument
Not yet done
Global solution
Proof
Limits
Complexity
Invariance
Smooth solutions
Limit equation
More precise solution
Comparison
Borg