Dispersion and moment lemmas revisited

I. Gasser; P. A. Markowich; B. Perthame

doi:10.1006/jdeq.1998.3595

Dispersion and moment lemmas revisited

I. Gasser^*, P. A. Markowich, B. Perthame

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

We further investigate relations between dispersive effects (like the Morawetz inequality) for various classical equations: Schrödinger, Dirac, and wave equations. After Wigner transform, these dispersive estimates are reduced to moment lemmas for kinetic equations. They yield new results for the Schrödinger (valid up to the semiclassical limit), wave, and Dirac equations; radial pseudo-differential operators; and also kinetic equations.

Original language	English (US)
Pages (from-to)	254-281
Number of pages	28
Journal	Journal of Differential Equations
Volume	156
Issue number	2
DOIs	https://doi.org/10.1006/jdeq.1998.3595
State	Published - Aug 10 1999
Externally published	Yes

Bibliographical note

Funding Information:
This research was supported by the German DAAD program PROCOPE ‘‘Verallgemeinerte Halbleitermodelle.’’ The first and the second author were also supported by Grant MA 1662 1-2 and 2-2 of the Deutsche Forschungsgemeinschaft.

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1006/jdeq.1998.3595

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author = "I. Gasser and Markowich, {P. A.} and B. Perthame",

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AU - Markowich, P. A.

AU - Perthame, B.

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PY - 1999/8/10

Y1 - 1999/8/10

N2 - We further investigate relations between dispersive effects (like the Morawetz inequality) for various classical equations: Schrödinger, Dirac, and wave equations. After Wigner transform, these dispersive estimates are reduced to moment lemmas for kinetic equations. They yield new results for the Schrödinger (valid up to the semiclassical limit), wave, and Dirac equations; radial pseudo-differential operators; and also kinetic equations.

AB - We further investigate relations between dispersive effects (like the Morawetz inequality) for various classical equations: Schrödinger, Dirac, and wave equations. After Wigner transform, these dispersive estimates are reduced to moment lemmas for kinetic equations. They yield new results for the Schrödinger (valid up to the semiclassical limit), wave, and Dirac equations; radial pseudo-differential operators; and also kinetic equations.

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DO - 10.1006/jdeq.1998.3595

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JO - Journal of Differential Equations

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ER -

Dispersion and moment lemmas revisited

Abstract

Bibliographical note

ASJC Scopus subject areas

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