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arXiv · 2511.15587

On the optimal local well-posedness of the wave kinetic equation in $L^r$

Ioakeim Ampatzoglou·Tristan Léger
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Abstract

In this paper, we give a unified treatment of the local well-posedness for the wave kinetic equation in almost critical weighted $L^r$ spaces with $2 \leq r \leq \infty.$ The proof builds on ideas from our earlier works \cite{AmLe24, AmLemain25}. Our approach is based solely on kinetic tools, with no appeal to Fourier theory.

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Ioakeim Ampatzoglou, Tristan Léger. 2025-11-19. On the optimal local well-posedness of the wave kinetic equation in $L^r$. https://doi.org/10.1016/j.jde.2026.114531

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