Derivation of a wave kinetic equation from the resonant-averaged stochastic NLS equation

作者：Kuksin Sergei; Maiocchi Alberto^*

来源：Physica D: Nonlinear Phenomena , 2015, 309: 65-70.

DOI：10.1016/j.physd.2015.04.002

• Weak turbulence
• Wave kinetic equation
• Kolmogorov-Zakharov spectra

We suggest a new derivation of a wave kinetic equation for the spectrum of the weakly nonlinear Schrodinger equation with stochastic forcing. The kinetic 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, analysed with full rigour in [8], 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 Kolmogorov-Zakharov spectra.

• 出版日期2015-8-1