On the wave turbulence theory for a stochastic KdV type equation--Generalization for the inhomogeneous kinetic limit

A Hannani, M Rosenzweig, G Staffilani… - arXiv preprint arXiv …, 2022 - arxiv.org
Starting from a stochastic Zakharov-Kuznetsov (ZK) equation on a lattice, the previous work
[ST21] by the last two authors gave a derivation of the homogeneous 3-wave kinetic …

Optimal local well-posedness theory for the kinetic wave equation

P Germain, AD Ionescu, MB Tran - Journal of Functional Analysis, 2020 - Elsevier
We prove local existence and uniqueness results for the (space-homogeneous) 4-wave
kinetic equation in wave turbulence theory. We consider collision operators defined by …

On the wave turbulence theory for a stochastic KdV type equation

G Staffilani, MB Tran - arXiv preprint arXiv:2106.09819, 2021 - arxiv.org
Starting from the stochastic Zakharov-Kuznetsov equation, a multidimensional KdV type
equation on a hypercubic lattice, we provide a derivation of the 3-wave kinetic equation. We …

[图书][B] Statistical physics of non equilibrium quantum phenomena

Y Pomeau, MB Tran - 2019 - Springer
The transition from Newtonian mechanics to quantum mechanics in the early years of the
twentieth century was a major step in the progress of our understanding of the world. This …

Almost sharp wave kinetic theory of multidimensional KdV type equations with

X Ma - arXiv preprint arXiv:2204.06148, 2022 - arxiv.org
In this work, we study the random series expansion of a multidimensional KdV type equation
with a diffusion term, the so-called Zakharov-Kuznetsov (ZK) equation. We impose random …

On the wave turbulence theory for stratified flows in the ocean

IM Gamba, LM Smith, MB Tran - Mathematical Models and Methods …, 2020 - World Scientific
After the pioneering work of Garrett and Munk, the statistics of oceanic internal gravity waves
has become a central subject of research in oceanography. The time evolution of the …

On the wave turbulence theory: ergodicity for the elastic beam wave equation

B Rumpf, A Soffer, MB Tran - arXiv preprint arXiv:2108.13223, 2021 - arxiv.org
Inspiring by a recent work [57], we analyse a 3-wave kinetic equation, derived from the
elastic beam wave equation on the lattice. The ergodicity condition states that two distinct …

A new paradigm for scattering theory of linear and nonlinear waves: review and open problems

A Soffer - Advances in Continuous and Discrete Models, 2024 - Springer
I present a review of the recent advancements in scattering theory, which provides a unified
approach to studying dispersive and hyperbolic equations with general interaction terms …

On the kinetic equation in Zakharov's wave turbulence theory for capillary waves

TT Nguyen, MB Tran - SIAM Journal on Mathematical Analysis, 2018 - SIAM
The wave turbulence equation is an effective kinetic equation that describes the dynamics of
wave spectra in weakly nonlinear and dispersive media. Such a kinetic model was derived …

Uniform in time lower bound for solutions to a quantum boltzmann equation of bosons

TT Nguyen, MB Tran - Archive for Rational Mechanics and Analysis, 2019 - Springer
In this paper, we consider a quantum Boltzmann equation, which describes the interaction
between excited atoms and a condensate. The collision integrals are taken–over energy …