Endpoint Strichartz Estimates

Endpoint Strichartz Estimates

We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension n ≥ 4) and the Schrödinger equation (in dimension n ≥ 3). Three other applications are discussed: local existence for a nonlinear wave equation; and Strichartz...

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Veröffentlicht in:American journal of mathematics 1998-10, Vol.120 (5), p.955-980
Hauptverfasser: Keel, Markus, Tao, Terence
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Estimation methods
Interpolation
Keels
Mathematical inequalities
Mathematical integrals
Mathematical theorems
Mathematics
Spacetime
Wave equations
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Beschreibung
Zusammenfassung:We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension n ≥ 4) and the Schrödinger equation (in dimension n ≥ 3). Three other applications are discussed: local existence for a nonlinear wave equation; and Strichartz-type estimates for more general dispersive equations and for the kinetic transport equation.
ISSN:0002-9327
1080-6377
1080-6377
DOI:10.1353/ajm.1998.0039