Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 283-326 |
| Number of pages | 44 |
| Journal | Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire |
| Volume | 35 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Mar 1 2018 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Analysis
- Mathematical Physics
Cite this
Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation. / Masaki, Satoshi; Segata, Junichi.
In: Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, Vol. 35, No. 2, 01.03.2018, p. 283-326.Research output: Contribution to journal › Article
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TY - JOUR
T1 - Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation
AU - Masaki, Satoshi
AU - Segata, Junichi
PY - 2018/3/1
Y1 - 2018/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85019096058&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85019096058&partnerID=8YFLogxK
U2 - 10.1016/j.anihpc.2017.04.003
DO - 10.1016/j.anihpc.2017.04.003
M3 - Article
VL - 35
SP - 283
EP - 326
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
SN - 0294-1449
IS - 2
ER -