On the kinetic equation in Zakharov's wave turbulence theory for capillary waves
  The wave turbulence equation is an effective kinetic equation that describes
the dynamics of wave spectrum in weakly nonlinear and dispersive media. Such a
kinetic model has been derived by physicists in the sixties, though the
well-posedness theory remains open, due to the complexity of resonant
interaction kernels. In this paper, we provide a global unique radial strong
solution, the first such a result, to the wave turbulence equation for
capillary waves.
