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

Vladimir Simeonov Gueorguiev, Bozhidar Velichkov

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

2 Citations (Scopus)

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 languageEnglish
Title of host publicationProgress in Mathematics
PublisherSpringer Basel
Pages145-162
Number of pages18
Volume301
DOIs
Publication statusPublished - 2012
Externally publishedYes

Publication series

NameProgress in Mathematics
Volume301
ISSN (Print)0743-1643
ISSN (Electronic)2296-505X

Fingerprint

Decay Estimates
3D
Non-negative
Nonlinearity
Generator
Analogue

Keywords

  • Decay estimates
  • Schrödinger equation
  • Semilinear

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Geometry and Topology

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

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

Gueorguiev, VS & Velichkov, B 2012, Decay estimates for the supercritical 3-D Schrödinger equation with rapidly decreasing potential. in 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
Gueorguiev VS, Velichkov B. Decay estimates for the supercritical 3-D Schrödinger equation with rapidly decreasing potential. In Progress in Mathematics. Vol. 301. Springer Basel. 2012. p. 145-162. (Progress in Mathematics). https://doi.org/10.1007/978-3-0348-0454-7_8
Gueorguiev, Vladimir Simeonov ; Velichkov, Bozhidar. / Decay estimates for the supercritical 3-D Schrödinger equation with rapidly decreasing potential. Progress in Mathematics. Vol. 301 Springer Basel, 2012. pp. 145-162 (Progress in Mathematics).
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