Strichartz estimates for the kinetic transport equation - Ovcharov, Evgeni Y. (SIAM journal on mathematical analysis, 2011)
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 Sér. 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.