Full derivation of the wave kinetic equation
We provide the rigorous derivation of the wave kinetic equation from the cubic nonlinear
Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that …
Schrödinger (NLS) equation at the kinetic timescale, under a particular scaling law that …
Propagation of chaos and higher order statistics in wave kinetic theory
The wave kinetic equation describes the effective dynamics of the second moments of the
Fourier modes of the NLS solution at the kinetic timescale, and in the kinetic limit in which …
Fourier modes of the NLS solution at the kinetic timescale, and in the kinetic limit in which …
Long time justification of wave turbulence theory
In a series of previous works (arxiv: 2104.11204, arxiv: 2110.04565, arxiv: 2301.07063), we
gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small …
gave a rigorous derivation of the homogeneous wave kinetic equation (WKE) up to small …
Stability and Cascades for the Kolmogorov–Zakharov Spectrum of Wave Turbulence
We consider the kinetic wave equation arising in wave turbulence to describe the Fourier
spectrum of solutions to the cubic Schrödinger equation. This equation has two Kolmogorov …
spectrum of solutions to the cubic Schrödinger equation. This equation has two Kolmogorov …
Inhomogeneous turbulence for the Wick Nonlinear Schrödinger equation
We introduce a simplified model for wave turbulence theory—the Wick nonlinear
Schrödinger equation, of which the main feature is the absence of all self‐interactions in the …
Schrödinger equation, of which the main feature is the absence of all self‐interactions in the …
Long time derivation of the Boltzmann equation from hard sphere dynamics
We provide a rigorous derivation of Boltzmann's kinetic equation from the hard-sphere
system for rarefied gas, which is valid for arbitrarily long time as long as the solution to the …
system for rarefied gas, which is valid for arbitrarily long time as long as the solution to the …
Local well-posedness for the kinetic mmt model
The MMT equation was proposed by Majda, McLaughlin and Tabak as a model to study
wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system …
wave turbulence. We focus on the kinetic equation associated to this Hamiltonian system …
Inhomogeneous turbulence for Wick NLS
We introduce a simplified model for wave turbulence theory--the Wick NLS, of which the
main feature is the absence of all self-interactions in the correlation expansions of its …
main feature is the absence of all self-interactions in the correlation expansions of its …
On the energy transfer towards large values of wavenumbers for solutions of 4-wave kinetic equations
Inspired by the fundamental work of Escobedo and Velazquez\cite {EscobedoVelazquez:
2015: FTB, EscobedoVelazquez: 2015: OTT}, we prove that solutions of 4-wave kinetic …
2015: FTB, EscobedoVelazquez: 2015: OTT}, we prove that solutions of 4-wave kinetic …
Condensation and non-condensation times for 4-wave kinetic equations
Inspired by the pioneering work of Escobedo and Velazquez\cite {EscobedoVelazquez:
2015: FTB, EscobedoVelazquez: 2015: OTT}, we prove that solutions of 4-wave kinetic …
2015: FTB, EscobedoVelazquez: 2015: OTT}, we prove that solutions of 4-wave kinetic …