About $L^p$ estimates for the spatially homogeneous Boltzmann equation

Details About $L^p$ estimates for the spatially homogeneous Boltzmann equation About $L^p$ estimates for the spatially homogeneous Boltzmann equation

2006-07-21

arxiv.org/abs/math/0607540v1

Annales de l'Institut Henri Poincar\'{e} Analyse non lin\'{e}aire 22 (2005) 127-142

Mathematics

Analysis of PDEs

19 pages

Scientific paper

10.1016/j.anihpc.2004.03.002

For the homogeneous Boltzmann equation with (cutoff or non cutoff) hard
potentials, we prove estimates of propagation of Lp norms with a weight $(1+
|x|^2)^q/2$ ($1 < p < +\infty$, $q \in \R\_+$ large enough), as well as
appearance of such weights. The proof is based on some new functional
inequalities for the collision operator, proven by elementary means.

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