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 …

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 …

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 …

The system that describes the dynamics of a Bose–Einstein Condensate (BEC) and the
thermal cloud at finite temperature consists of a nonlinear Schrodinger (NLS) and a quantum …

In weak turbulence theory, the Kolmogorov–Zakharov spectra is a class of time-independent
solutions to the kinetic wave equations. In this paper, we construct a new class of time …

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 …

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 …

We propose a new approach to study the long time dynamics of the wave kinetic equation in
the statistical description of acoustic turbulence. The approach is based on rewriting the …

We consider in this paper a system coupling a linear quantum Boltzmann equation and a
defocussing cubic nonlinear Schrödinger equation. The Schrodinger equation reflects the …

When the temperature of a trapped Bose gas is below the Bose-Einstein transition
temperature and above absolute zero, the gas is composed of two distinct components: the …