A new approach to velocity averaging lemmas in Besov spaces

2012/06/28 by Diogo Arsénio, Nader Masmoudi, Arsénio, Diogo +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.1206.6659

63 pages

arxiv created 2012/06/28 · arxiv updated 2012/06/29

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≤ p. We also establish results on the control of concentrations in the degenerate L_x,v¹ case, which is fundamental in the study of the hydrodynamic limit of the Boltzmann equation.

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