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Mathematical Physics Seminar

Proof of the Energy Cascade Conjecture of Weak Turbulence Theory

Avy Soffer -- Rutgers University 

Location:  Hill 705
Date & time: Thursday, 06 December 2018 at 2:00PM - 3:00PM

Abstract:   In weak turbulence theory, the Kolmogorov-Zakharov spectra is a class of time-independent solutions to the 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 wavenumbers to large wave  numbers. The energy of the system is concentrated at {p = ?} and the energy function becomes a Dirac function at in?nity.
The existence of this class of solutions is a rigorous mathematical proof based on the kinetic description for the energy cascade phenomenon.