### 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 |
---|---|

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 |
---|---|

Volume | 301 |

ISSN (Print) | 0743-1643 |

ISSN (Electronic) | 2296-505X |

### Fingerprint

### Keywords

- Decay estimates
- Schrödinger equation
- Semilinear

### ASJC Scopus subject areas

- Algebra and Number Theory
- Analysis
- Geometry and Topology

### Cite this

*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

**Decay estimates for the supercritical 3-D Schrödinger equation with rapidly decreasing potential.** / Gueorguiev, Vladimir Simeonov; Velichkov, Bozhidar.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Decay estimates for the supercritical 3-D Schrödinger equation with rapidly decreasing potential

AU - Gueorguiev, Vladimir Simeonov

AU - Velichkov, Bozhidar

PY - 2012

Y1 - 2012

N2 - 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.

AB - 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.

KW - Decay estimates

KW - Schrödinger equation

KW - Semilinear

UR - http://www.scopus.com/inward/record.url?scp=85028068615&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85028068615&partnerID=8YFLogxK

U2 - 10.1007/978-3-0348-0454-7_8

DO - 10.1007/978-3-0348-0454-7_8

M3 - Chapter

VL - 301

T3 - Progress in Mathematics

SP - 145

EP - 162

BT - Progress in Mathematics

PB - Springer Basel

ER -