TY - JOUR

T1 - Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation

AU - Masaki, Satoshi

AU - Segata, Jun ichi

N1 - Funding Information:
The part of this work was done while the authors were visiting at Department of Mathematics at the University of California, Santa Barbara whose hospitality they gratefully acknowledge. S.M. is partially supported by JSPS , Grant-in-Aid for Young Scientists (B) 24740108 . J.S. is partially supported by JSPS , Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation and by JSPS , Grant-in-Aid for Young Scientists (A) 25707004 .
Funding Information:
The part of this work was done while the authors were visiting at Department of Mathematics at the University of California, Santa Barbara whose hospitality they gratefully acknowledge. S.M. is partially supported by JSPS, Grant-in-Aid for Young Scientists (B) 24740108. J.S. is partially supported by JSPS, Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation and by JSPS, Grant-in-Aid for Young Scientists (A) 25707004.

PY - 2018/3

Y1 - 2018/3

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.

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U2 - 10.1016/j.anihpc.2017.04.003

DO - 10.1016/j.anihpc.2017.04.003

M3 - Article

AN - SCOPUS:85019096058

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 -