@article{75eec5a0bd4f44eaafa0ed3cedba9bd6,
title = "On the kinetic equation in zakharov's wave turbulence theory for capillary waves",
abstract = "The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave spectra in weakly nonlinear and dispersive media. Such a kinetic model was derived by physicists in the 1960s, though the well-posedness theory remains open due to the complexity of resonant interaction kernels. In this paper, we provide a global unique radial strong solution-the first such result-to the wave turbulence equation for capillary waves.",
author = "Nguyen, {Toan T.} and Tran, {Minh Binh}",
note = "Funding Information: ∗Received by the editors April 10, 2017; accepted for publication (in revised form) January 22, 2018; published electronically April 10, 2018. http://www.siam.org/journals/sima/50-2/M112504.html Funding: The research of the first author was partially supported by NSF grant DMS-1405728. The research of the second author was supported by NSF grant RNMS (Ki-Net) 1107291 and ERC Advanced grant DYCON. †Department of Mathematics, Pennsylvania State University, State College, PA 16802 (nguyen@ math.psu.edu). ‡Department of Mathematics, University of Wisconsin-Madison, Madison, WI 53706 (mtran23@ wisc.edu). Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics.",
year = "2018",
doi = "10.1137/17M1125042",
language = "English (US)",
volume = "50",
pages = "2020--2047",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",
}