Global well-posedness of partially periodic KP-I equation in the energy space and application

Robert, Tristan

doi:10.1016/j.anihpc.2018.03.002

Robert, Tristan

Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 7, pp. 1773-1826

Voir la notice de l'article provenant de la source Numdam

Résumé

In this article, we address the Cauchy problem for the KP-I equation

\partial_{t} u + \partial_{x}^{3} u - \partial_{x}^{- 1} \partial_{y}^{2} u + u \partial_{x} u = 0

for functions periodic in y. We prove global well-posedness of this problem for any data in the energy space

E = {u \in L^{2} (R \times T), \partial_{x} u \in L^{2} (R \times T), \partial_{x}^{- 1} \partial_{y} u \in L^{2} (R \times T)}

. We then prove that the KdV line soliton, seen as a special solution of KP-I equation, is orbitally stable under this flow, as long as its speed is small enough.

MR Zbl

DOI : 10.1016/j.anihpc.2018.03.002

Keywords: Kadomtsev–Petviashvili equation, Global well-posedness, Orbital stability, KdV line soliton

@article{AIHPC_2018__35_7_1773_0,
     author = {Robert, Tristan},
     title = {Global well-posedness of partially periodic {KP-I} equation in the energy space and application},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1773--1826},
     publisher = {Elsevier},
     volume = {35},
     number = {7},
     year = {2018},
     doi = {10.1016/j.anihpc.2018.03.002},
     mrnumber = {3906856},
     zbl = {1404.35106},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.03.002/}
}

TY  - JOUR
AU  - Robert, Tristan
TI  - Global well-posedness of partially periodic KP-I equation in the energy space and application
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2018
SP  - 1773
EP  - 1826
VL  - 35
IS  - 7
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.03.002/
DO  - 10.1016/j.anihpc.2018.03.002
LA  - en
ID  - AIHPC_2018__35_7_1773_0
ER  -

%0 Journal Article
%A Robert, Tristan
%T Global well-posedness of partially periodic KP-I equation in the energy space and application
%J Annales de l'I.H.P. Analyse non linéaire
%D 2018
%P 1773-1826
%V 35
%N 7
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2018.03.002/
%R 10.1016/j.anihpc.2018.03.002
%G en
%F AIHPC_2018__35_7_1773_0

Robert, Tristan. Global well-posedness of partially periodic KP-I equation in the energy space and application. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 7, pp. 1773-1826. doi: 10.1016/j.anihpc.2018.03.002

Cité par Sources :

Parcourir par

Geodesic

Parcourir par