# 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.

**Synopsis:**

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.