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arXiv · 1711.05587

Optimal local well-posedness theory for the kinetic wave equation

Pierre Germain·Alexandru D. Ionescu·Minh-Binh Tran
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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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Pierre Germain, Alexandru D. Ionescu, Minh-Binh Tran. 2017-11-15. Optimal local well-posedness theory for the kinetic wave equation. https://arxiv.org/abs/1711.05587

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