Gigliola Staffilani: Some recent developments in wave turbulence theory

Abstract: In this talk I will present two different approaches in the study of wave turbulence theory. The first, introduced by Bourgain, consists in analyzing the long time behavior of high Sobolev norms for the defocusing, cubic NLS equation on 2D tori (periodic solutions). In this context I will emphasize how the rationality or irrationality of the torus affects the analysis. The second approach deals with the rigorous derivation of the 3-wave kinetic equation from a weakly nonlinear multidimensional KdV type equation.
Gigliola Staffilani is an Italian-American mathematician who works as the Abby Rockefeller Mauze Professor of Mathematics at the Massachusetts Institute of Technology. Her research concerns harmonic analysis and partial differential equations, including the Korteweg-de Vries equation and Schrödinger equation.
This lecture was part of the bi-annual Abel Symposium.
This year the title of the symposium was Partial Differential Equations waves, Nonlinearities and Nonlocalities.
The symposium was funded by
- The Norwegian Academy of Sciences and Letters via the Abel board and The Norwegian Mathematical Society
- NTNU Norwegian University of Science and Technology
- Research Council of Norway via the grant Waves and Nonlinear Phenomena
- Trond Mohn Foundation

Hi. For Gigliola Staffilani: The question if the velocities are bound at any time is a fundamental question also for the Navier Stokes solutions. Do you think to connect in some way the solutions in the problem you expose to the NS problem later?