Seminar

Zoom Link

In this talk we will use the periodic cubic nonlinear Schrödinger equation to present some estimates relative to  the long time dynamics of the energy spectrum, a fundamental object in the study of wave turbulence theory. Going back to Bourgain, one possible way to conduct the analysis is to look at the growth of high Sobolev norms. It turns out that this growth is sensitive to the nature of the space periodicity of the system. I will present a combination of old and very recent results in this direction.  In the second part of the talk I will show how under  certain conditions one can derive an effective equation governing the dynamics of the energy spectrum, this is the wave kinetic equation (WKE). I will conclude with a recent result on energy transfer obtained using the WKE.