2013/11/26 by Sergei Kuksin, Kuksin, Sergei, Alberto Maiocchi +1
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Meteorological Phenomena and Simulations #math-ph #math.MP #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1311.6794
openalex publication_date 2013/11/26 · arxiv created 2013/12/26 · arxiv updated 2013/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We suggest a new derivation of a kinetic equation of Kolmogorov-Zakharov (KZ) type for the spectrum of the weakly nonlinear Schrödinger equation with stochastic forcing. The kynetic equation is obtained as a result of a double limiting procedure. Firstly, we consider the equation on a finite box with periodic boundary conditions and send the size of the nonlinearity and of the forcing to zero, while the time is correspondingly rescaled; then, the size of the box is sent to infinity (with a suitable rescaling of the solution). We report here the results of the first limiting procedure, analyzed with full rigour in arXiv:1311.6793, and show how the second limit leads to a kinetic equation for the spectrum, if some further hypotheses (commonly employed in the weak turbulence theory) are accepted. Finally we show how to derive from these equations the KZ spectra.