Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Tohru Ozawa, Jian Zhai (2008)
Annales de l'I.H.P. Analyse non linéaire
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S. A. Denisov (2010)
Mathematical Modelling of Natural Phenomena
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In this short note, we apply the technique developed in [Math. Model. Nat. Phenom., 5 (2010), No. 4, 122-149] to study the long-time evolution for Schrödinger equation with slowly decaying potential.
Patrick Gérard, Vittoria Pierfelice (2010)
Bulletin de la Société Mathématique de France
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We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadratic nonlinearities as well as a necessary and sufficient condition of global well-posedness...
Mejjaoli, H. (2009)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 35Q55,42B10. In this paper, we study the Schrödinger equation associated with the Dunkl operators, we study the dispersive phenomena and we prove the Strichartz estimates for this equation. Some applications are discussed.
Antonio Ambrosetti (2008)
Bollettino dell'Unione Matematica Italiana
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We survey some recent results dealing with some classes of systems of nonlinear Schrödinger equations.
Changxing Miao, Youbin Zhu (2006)
Annales Polonici Mathematici
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We consider the Cauchy problem for a generalized Klein-Gordon-Schrödinger system with Yukawa coupling. We prove the existence of global weak solutions by the compactness method and, through a special choice of the admissible pairs to match two types of equations, we prove the uniqueness of those solutions by an approach similar to the method presented by J. Ginibre and G. Velo for the pure Klein-Gordon equation or pure Schrödinger equation. Though it is very simple in form, the method...
Nakao Hayashi, Masayoshi Tsutsumi (1981)
Mathematische Zeitschrift
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Filip Ficek (2023)
Archivum Mathematicum
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Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials. ...
Nakao Hayashi, Keiichi Kato, Pavel I. Naumkin (1998)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Zhengping Wang, Huan-Song Zhou (2009)
Journal of the European Mathematical Society
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