Title: On the kinetic equation in Zakharov's wave turbulence theory for capillary waves,
Abstract: 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.