$L^p$-estimates of the Botlzmann Equation around a traveling local Maxwellian

Details $L^p$-estimates of the Botlzmann Equation around a traveling local Maxwellian $L^p$-estimates of the Botlzmann Equation around a traveling local Maxwellian

2010-09-26

arxiv.org/abs/1009.5091v1

Mathematics

Analysis of PDEs

11 pages

Scientific paper

In this paper, we are interested in the $L^p$-estimates of the Boltzmann equation in the case that the distribution function stays around a travelling local Maxwellian. For this, we divide both sides of the Boltzmann equation by the velocity distribution function with a fractional exponent and reformulate the Boltzmann equation into a regularized one. This amounts to endowing additional integrability on the collision kernel, which in turn enables us to apply simple H\"{o}lder type inequalities. Our results cover the whole range of Lebesgue exponents: $0

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