Growth of sobolev norms for the cubic defocusing NLS with a convolution potential
Fix s > 1. Colliander et al. proved in (Invent Math 181:39–113, 2010 )the existence of solutions of the cubic defocusing nonlinear Schrödinger equation in the two torus whose s -Sobolev norm undergoes arbitrarily large growth as time evolves. In this paper we generalize their result to the cubic...
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/113915 |
| Acceso en línea: | https://hdl.handle.net/2117/113915 https://dx.doi.org/10.1007/s00220-014-1977-1 |
| Access Level: | acceso abierto |
| Palabra clave: | Schrödinger equation Schrödinger, Equació de Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | Fix s > 1. Colliander et al. proved in (Invent Math 181:39–113, 2010 )the existence of solutions of the cubic defocusing nonlinear Schrödinger equation in the two torus whose s -Sobolev norm undergoes arbitrarily large growth as time evolves. In this paper we generalize their result to the cubic defocusing nonlinear Schrödinger equation with a convolution potential. Moreover, we show that the speed of growth is the same as the one obtained for the cubic defocusing nonlinear Schrödinger equation in Guardia and Kaloshin (Growth of Sobolev norms in the cubic defocusing Nonlinear Schrödinger Equation. To appear in the Journal of the European Mathematical Society, 2012 ) |
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