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 |
Keywords
- Decay estimates
- Schrödinger equation
- Semilinear
ASJC Scopus subject areas
- Algebra and Number Theory
- Analysis
- Geometry and Topology
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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