Geodesic
Global solutions for the gravity water waves equation in dimension 3
Pierre Germain1 ; Nader Masmoudi2 ; Jalal Shatah2
1 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012
2 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012
Annals of mathematics, Tome 175 (2012) no. 2, pp. 691-754.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We show existence of global solutions for the gravity water waves equation in dimension 3, in the case of small data. The proof combines energy estimates, which yield control of $L^2$ related norms, with dispersive estimates, which give decay in $L^\infty$. To obtain these dispersive estimates, we use an analysis in Fourier space; the study of space and time resonances is then the crucial point.
DOI : 10.4007/annals.2012.175.2.6

Pierre Germain 1 ; Nader Masmoudi 2 ; Jalal Shatah 2

1 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012
2 Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY 10012 
@article{10_4007_annals_2012_175_2_6,
     author = {Pierre Germain and Nader Masmoudi and Jalal Shatah},
     title = {Global solutions for the gravity water waves equation in dimension 3},
     journal = {Annals of mathematics},
     pages = {691--754},
     publisher = {mathdoc},
     volume = {175},
     number = {2},
     year = {2012},
     doi = {10.4007/annals.2012.175.2.6},
     mrnumber = {2993751},
     zbl = {06025001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.2.6/}
}
TY  - JOUR
AU  - Pierre Germain
AU  - Nader Masmoudi
AU  - Jalal Shatah
TI  - Global solutions for the gravity water waves equation in dimension 3
JO  - Annals of mathematics
PY  - 2012
SP  - 691
EP  - 754
VL  - 175
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.2.6/
DO  - 10.4007/annals.2012.175.2.6
LA  - en
ID  - 10_4007_annals_2012_175_2_6
ER  - 
%0 Journal Article
%A Pierre Germain
%A Nader Masmoudi
%A Jalal Shatah
%T Global solutions for the gravity water waves equation in dimension 3
%J Annals of mathematics
%D 2012
%P 691-754
%V 175
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.2.6/
%R 10.4007/annals.2012.175.2.6
%G en
%F 10_4007_annals_2012_175_2_6
Pierre Germain; Nader Masmoudi; Jalal Shatah. Global solutions for the gravity water waves equation in dimension 3. Annals of mathematics, Tome 175 (2012) no. 2, pp. 691-754. doi : 10.4007/annals.2012.175.2.6. http://geodesic.mathdoc.fr/articles/10.4007/annals.2012.175.2.6/

Cité par Sources :