### On the Hasselmann-Zakharov’s weak turbulence equation for capillary waves

In this paper with M.-B. Tran, we construct solutions to the following weak turbulence kinetic equation for capillary waves (cf. Hasselmann ’62, Zakharov ’67): describing the dynamics of wave density at wavenumber , . Here, denotes the positive coefficient of fluid viscosity, and is the collision term, describing pure resonant three-wave interactions: with , with…