### Abstract

We establish an almost optimal decay estimate for the 3-D Schrödinger equation with non-negative potential decaying exponentially and nonlinearity of power p > 1 + 2/3 = 5/3. The key point is the introduction of an appropriate analogue of the generators of the pseudoconformal group for the free Schrödinger equation.

Original language | English |
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Title of host publication | Progress in Mathematics |

Publisher | Springer Basel |

Pages | 145-162 |

Number of pages | 18 |

Volume | 301 |

DOIs | |

Publication status | Published - 2012 |

Externally published | Yes |

### Publication series

Name | Progress in Mathematics |
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Volume | 301 |

ISSN (Print) | 0743-1643 |

ISSN (Electronic) | 2296-505X |

### Keywords

- Decay estimates
- Schrödinger equation
- Semilinear

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Geometry and Topology

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## Cite this

Gueorguiev, V. S., & Velichkov, B. (2012). Decay estimates for the supercritical 3-D Schrödinger equation with rapidly decreasing potential. In

*Progress in Mathematics*(Vol. 301, pp. 145-162). (Progress in Mathematics; Vol. 301). Springer Basel. https://doi.org/10.1007/978-3-0348-0454-7_8