STRICHARTZ ESTIMATES FOR THE KINETIC TRANSPORT EQUATION

STRICHARTZ ESTIMATES FOR THE KINETIC TRANSPORT EQUATION

In this paper we prove new Strichartz estimates for the kinetic transport equation and carry out a detailed investigation on their range of validity. In one spatial dimension we find essentially all possible estimates, while in higher dimensions some endpoint and inhomogeneous estimates remain open....

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Veröffentlicht in:SIAM journal on mathematical analysis 2011-01, Vol.43 (3-4), p.1282-1310
1. Verfasser: OVCHAROV, Evgeni Y
Format: Artikel
Sprache:eng
Schlagworte:
Estimates
Exact sciences and technology
Keels
Mathematical analysis
Mathematics
Paris
Sciences and techniques of general use
Studies
Transport equations
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Zusammenfassung:In this paper we prove new Strichartz estimates for the kinetic transport equation and carry out a detailed investigation on their range of validity. In one spatial dimension we find essentially all possible estimates, while in higher dimensions some endpoint and inhomogeneous estimates remain open. The Strichartz estimates that we present extend previous results by Castella and Perthame [C. R. Acad. Sci. Paris Ser. I Math., 322 (1996), pp. 535-540] and Keel and Tao [Amer. J. Math., 120 (1998), pp. 955-980]. Our work generalizes the techniques of Foschi [J. Hyperbolic Differ. Equ., 2 (2005), pp. 1-24] for proving inhomogeneous Strichartz estimates to the context of the kinetic transport equation. [PUBLICATION ABSTRACT]
ISSN:0036-1410
1095-7154
DOI:10.1137/100803808