Estimates for the Boltzmann collision operator via radial symmetry and Fourier transform

Details Estimates for the Boltzmann collision operator via radial symmetry and Fourier transform Estimates for the Boltzmann collision operator via radial symmetry and Fourier transform

2008-12-16

arxiv.org/abs/0812.3168v2

Advances in Mathematics (New York. 1965), v. 223, p. 511-528, 2010

Mathematics

Analysis of PDEs

14 pages

Scientific paper

10.1016/j.aim.2009.08.017

We extend the $L^p$-theory of the Boltzmann collision operator by using classical techniques based in the Carleman representation and Fourier analysis, allied to new ideas that exploit the radial symmetry of this operator. We are then able to greatly simplify existent technical proofs in this theory, extend the range, and obtain explicit sharp constants in some convolution-like inequalities for the gain part of the Boltzmann collision operator.

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