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arXiv · 1206.6659

A new approach to velocity averaging lemmas in {B}esov spaces

Diogo Arsénio·Nader Masmoudi
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Abstract

We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results, which display, in some cases, a gain of one full derivative. Moreover, the study of dispersion allows to treat the case of $L_x^rL^p_v$ integrability with $r\leq p$. We also establish results on the control of concentrations in the degenerate $L_{x,v}^1$ case, which is fundamental in the study of the hydrodynamic limit of the Boltzmann equation.

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Diogo Arsénio, Nader Masmoudi. 2012-06-28. A new approach to velocity averaging lemmas in {B}esov spaces. https://arxiv.org/abs/1206.6659

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