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 |
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Keywords
- Decay estimates
- Schrödinger equation
- Semilinear
ASJC Scopus subject areas
- Algebra and Number Theory
- Analysis
- Geometry and Topology
Cite this
Decay estimates for the supercritical 3-D Schrödinger equation with rapidly decreasing potential. / Gueorguiev, Vladimir Simeonov; Velichkov, Bozhidar.
Progress in Mathematics. Vol. 301 Springer Basel, 2012. p. 145-162 (Progress in Mathematics; Vol. 301).Research output: Chapter in Book/Report/Conference proceeding › Chapter
}
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
AN - SCOPUS:85028068615
VL - 301
T3 - Progress in Mathematics
SP - 145
EP - 162
BT - Progress in Mathematics
PB - Springer Basel
ER -