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On the kinetic equation in Zakharov's wave turbulence theory for capillary waves (1702.03892v2)
Published 13 Feb 2017 in math.AP, math-ph, math.MP, and physics.flu-dyn
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.
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