Analysis Seminar

Proof of the Energy Cascade Conjecture of Weak Turbulence Theory

Speaker: Avy SOFFER, Rutgers

Location: Warren Weaver Hall 1302

Date: Thursday, October 10, 2019, 11 a.m.


In weak turbulence theory, the Kolmogorov-Zakharovspectra is a class of
time-independent solutions to kinetic wave equations. In this work we
construct a new class of time-dependent solutions to those kinetic
equations. These solutions exhibit the interesting property that  ALL
the energy is cascaded from small wave numbers to large wave numbers.

The energy of the system is concentrated at {p=∞} and the energy
function becomes a Dirac delta function at infinity.

The existence of this class  of solutions is a rigorous mathematical proof based on the kinetic
description for the energy  cascade phenomenon.