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Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg–de Vries equation.
- Source :
-
Annales de l'Institut Henri Poincaré C . Mar2018, Vol. 35 Issue 2, p283-326. 44p. - Publication Year :
- 2018
-
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 L ˆ r space where L ˆ r = { f ∈ S ′ ( R ) | ‖ f ‖ L ˆ r = ‖ f ˆ ‖ L r ′ < ∞ } . We construct this solution by a concentration compactness argument. Then, key ingredients are a linear profile decomposition result adopted to L ˆ r -framework and approximation of solutions to the gKdV equation which involves rapid linear oscillation by means of solutions to the nonlinear Schrödinger equation. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02941449
- Volume :
- 35
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Annales de l'Institut Henri Poincaré C
- Publication Type :
- Academic Journal
- Accession number :
- 128348106
- Full Text :
- https://doi.org/10.1016/j.anihpc.2017.04.003