Cauchy theory for the gravity water waves system with non-localized initial data
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 337-395
Voir la notice de l'article provenant de la source Numdam
In this article, we develop the local Cauchy theory for the gravity water waves system, for rough initial data which do not decay at infinity. We work in the context of -based uniformly local Sobolev spaces introduced by Kato [22]. We prove a classical well-posedness result (without loss of derivatives). Our result implies also a local well-posedness result in Hölder spaces (with loss of derivatives). As an illustration, we solve a question raised by Boussinesq in [9] on the water waves problem in a canal. We take benefit of an elementary observation to show that the strategy suggested in [9] does indeed apply to this setting.
DOI :
10.1016/j.anihpc.2014.10.004
Keywords:
Water-waves, Cauchy problem, Uniformly local Sobolev spaces, Paradifferential calculus
@article{AIHPC_2016__33_2_337_0,
author = {Alazard, T. and Burq, N. and Zuily, C.},
title = {Cauchy theory for the gravity water waves system with non-localized initial data},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {337--395},
publisher = {Elsevier},
volume = {33},
number = {2},
year = {2016},
doi = {10.1016/j.anihpc.2014.10.004},
zbl = {1339.35227},
mrnumber = {3465379},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.10.004/}
}
TY - JOUR AU - Alazard, T. AU - Burq, N. AU - Zuily, C. TI - Cauchy theory for the gravity water waves system with non-localized initial data JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 337 EP - 395 VL - 33 IS - 2 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.10.004/ DO - 10.1016/j.anihpc.2014.10.004 LA - en ID - AIHPC_2016__33_2_337_0 ER -
%0 Journal Article %A Alazard, T. %A Burq, N. %A Zuily, C. %T Cauchy theory for the gravity water waves system with non-localized initial data %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 337-395 %V 33 %N 2 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2014.10.004/ %R 10.1016/j.anihpc.2014.10.004 %G en %F AIHPC_2016__33_2_337_0
Alazard, T.; Burq, N.; Zuily, C. Cauchy theory for the gravity water waves system with non-localized initial data. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 2, pp. 337-395. doi: 10.1016/j.anihpc.2014.10.004
Cité par Sources :