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

Ioakeim Ampatzoglou; Tristan Léger

doi:10.1016/j.jde.2026.114531

paper

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

arXiv:2511.15587 · doi:10.1016/j.jde.2026.114531

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.

26 pages

On the optimal local well-posedness of the wave kinetic equation in Lr

Abstract

References in corpus (3)

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