Optimal local well-posedness theory for the kinetic wave equation

By Pierre Germain, A. Ionescu, Minh-Binh Tran. Journal of Functional Analysis, 2017

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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.

Subfields: Applied Mathematics, Mathematical Physics

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