Voir la notice de l'article provenant de la source Numdam
This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on global solutions for small and localized data. Such solutions have been proved to exist in Ionescu– Pusateri [Invent. Math. 199 (2015)], Alazard–Delort [Ann. Sci. Éc. Norm. Supér. (4) 48 (2015)], Hunter et al. [Comm. Math. Phys. 346 (2016)], and Ifrim–Tataru [Bull. Soc. Math. France 144 (2016)] in much higher regularity. Our goal in this paper is to improve these results and prove global well-posedness under minimal regularity and decay assumptions for the initial data. One key ingredient here is represented by the balanced cubic estimates in our first paper. Another is the nonlinear vector field Sobolev inequalities, an idea first introduced by Ifrim–Tataru [Ann. Sci. Éc. Norm. Supér. (4) 52 (2019)] in the context of the Benjamin–Ono equations.
@article{AIHPC_2022__39_4_819_0,
author = {Ai, Albert and Ifrim, Mihaela and Tataru, Daniel},
title = {Two-dimensional gravity waves at low regularity {II:} {Global} solutions},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {819--884},
volume = {39},
number = {4},
year = {2022},
doi = {10.4171/aihpc/21},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/21/}
}
TY - JOUR AU - Ai, Albert AU - Ifrim, Mihaela AU - Tataru, Daniel TI - Two-dimensional gravity waves at low regularity II: Global solutions JO - Annales de l'I.H.P. Analyse non linéaire PY - 2022 SP - 819 EP - 884 VL - 39 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4171/aihpc/21/ DO - 10.4171/aihpc/21 LA - en ID - AIHPC_2022__39_4_819_0 ER -
%0 Journal Article %A Ai, Albert %A Ifrim, Mihaela %A Tataru, Daniel %T Two-dimensional gravity waves at low regularity II: Global solutions %J Annales de l'I.H.P. Analyse non linéaire %D 2022 %P 819-884 %V 39 %N 4 %U http://geodesic.mathdoc.fr/articles/10.4171/aihpc/21/ %R 10.4171/aihpc/21 %G en %F AIHPC_2022__39_4_819_0
Ai, Albert; Ifrim, Mihaela; Tataru, Daniel. Two-dimensional gravity waves at low regularity II: Global solutions. Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 4, pp. 819-884. doi: 10.4171/aihpc/21
Cité par Sources :