Geodesic
Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 283-326

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

In this article, we prove the existence of a non-scattering solution, which is minimal in some sense, to the mass-subcritical generalized Korteweg–de Vries (gKdV) equation in the scale critical Lˆr space where Lˆr={f∈S′(R)|‖f‖Lˆr=‖fˆ‖Lr′<∞}. We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to Lˆr-framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schrödinger equation.

DOI : 10.1016/j.anihpc.2017.04.003
Classification : 35Q53, 35B40, 35B30
Keywords: Generalized Korteweg–de Vries equation, Scattering problem, Threshold solution 
@article{AIHPC_2018__35_2_283_0,
     author = {Masaki, Satoshi and Segata, Jun-ichi},
     title = {Existence of a minimal non-scattering solution to the mass-subcritical generalized {Korteweg{\textendash}de} {Vries} equation},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {283--326},
     publisher = {Elsevier},
     volume = {35},
     number = {2},
     year = {2018},
     doi = {10.1016/j.anihpc.2017.04.003},
     mrnumber = {3765544},
     zbl = {1383.35196},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.04.003/}
}
TY  - JOUR
AU  - Masaki, Satoshi
AU  - Segata, Jun-ichi
TI  - Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2018
SP  - 283
EP  - 326
VL  - 35
IS  - 2
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.04.003/
DO  - 10.1016/j.anihpc.2017.04.003
LA  - en
ID  - AIHPC_2018__35_2_283_0
ER  - 
%0 Journal Article
%A Masaki, Satoshi
%A Segata, Jun-ichi
%T Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation
%J Annales de l'I.H.P. Analyse non linéaire
%D 2018
%P 283-326
%V 35
%N 2
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2017.04.003/
%R 10.1016/j.anihpc.2017.04.003
%G en
%F AIHPC_2018__35_2_283_0
Masaki, Satoshi; Segata, Jun-ichi. Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 2, pp. 283-326. doi: 10.1016/j.anihpc.2017.04.003

Cité par Sources :