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The periodic nonlinear Schrodinger (NLS) equations: deterministic and probabilistic approaches

External Lecturer: 
Prof. Gigliola Staffilani
Course Type: 
PhD Course
Academic Year: 
2021-2022
Period: 
June 20th - July 5th
Duration: 
20 h
Description: 

In this course we will study different aspects of the nonlinear and periodic Schrodinger equation, mainly in 2D. We start with Strichartz estimates for the deterministic well-posedness, we then introduce the notion of transfer of energy, and we present few theorems concerning this very active area of research. We then move to the notion of Gibbs measure and its invariance. If we have time we introduce the wave kinetic equation associated to the NLS as well.

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