@article{2ff83f0372ec409a8a6319ff92f9e0d0,
title = "Optimal local well-posedness theory for the kinetic wave equation",
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.",
keywords = "Nonlinear Schr{\"o}dinger, Quantum Boltzmann, Wave (weak) turbulence, Wave kinetic equations",
author = "Pierre Germain and Ionescu, {Alexandru D.} and Tran, {Minh Binh}",
note = "Funding Information: PG was supported by the National Science Foundation grant DMS-1301380 . ADI was supported in part by NSF grant DMS-1600028 and by NSF-FRG grant DMS-1463753 . MBT was supported by NSF Grant DMS-1814149 , NSF Grant DMS-1854453 , SMU URC Grant 2020 , Linking Fellowship of Dedman College of Humanities and Sciences and Alexander von Humboldt Research Fellowship of Alexander von Humboldt Foundation. The authors would like to thank Sergey Nazarenko and Alan Newell for fruitful discussions on the topic. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",
year = "2020",
month = sep,
day = "1",
doi = "10.1016/j.jfa.2020.108570",
language = "English (US)",
volume = "279",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press Inc.",
number = "4",
}