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Optimal local well-posedness theory for the kinetic wave equation (1711.05587v2)
Published 15 Nov 2017 in math.AP
Abstract: We prove local existence and uniqueness results for the (space-homogeneous) 4-wave kinetic equation in wave turbulence theory. We consider collision operators defined by radial, but general dispersion relations satisfying suitable bounds, and we prove two local well-posedness theorems in nearly critical weighted spaces.
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