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 in critical Besov spaces, which display, in some cases, a gain of one full derivative. Moreover, the study of dispersion allows to treat the case of LxrLvp integrability with r ≤ p. We also establish results on the control of concentrations in the degenerate Lx,v1 case, which is fundamental in the study of hydrodynamic limits of the Boltzmann equation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 495-551 |
| Number of pages | 57 |
| Journal | Journal des Mathematiques Pures et Appliquees |
| Volume | 101 |
| Issue number | 4 |
| DOIs | |
| State | Published - 2014 |
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Keywords
- Besov spaces
- Dispersion
- Kinetic transport equation
- Velocity averaging
ASJC Scopus subject areas
- Applied Mathematics
- Mathematics(all)
Cite this
A new approach to velocity averaging lemmas in Besov spaces. / Arsénio, Diogo; Masmoudi, Nader.
In: Journal des Mathematiques Pures et Appliquees, Vol. 101, No. 4, 2014, p. 495-551.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A new approach to velocity averaging lemmas in Besov spaces
AU - Arsénio, Diogo
AU - Masmoudi, Nader
PY - 2014
Y1 - 2014
N2 - 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 in critical Besov spaces, which display, in some cases, a gain of one full derivative. Moreover, the study of dispersion allows to treat the case of LxrLvp integrability with r ≤ p. We also establish results on the control of concentrations in the degenerate Lx,v1 case, which is fundamental in the study of hydrodynamic limits of the Boltzmann equation.
AB - 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 in critical Besov spaces, which display, in some cases, a gain of one full derivative. Moreover, the study of dispersion allows to treat the case of LxrLvp integrability with r ≤ p. We also establish results on the control of concentrations in the degenerate Lx,v1 case, which is fundamental in the study of hydrodynamic limits of the Boltzmann equation.
KW - Besov spaces
KW - Dispersion
KW - Kinetic transport equation
KW - Velocity averaging
UR - http://www.scopus.com/inward/record.url?scp=84896387740&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84896387740&partnerID=8YFLogxK
U2 - 10.1016/j.matpur.2013.06.012
DO - 10.1016/j.matpur.2013.06.012
M3 - Article
AN - SCOPUS:84896387740
VL - 101
SP - 495
EP - 551
JO - Journal des Mathematiques Pures et Appliquees
JF - Journal des Mathematiques Pures et Appliquees
SN - 0021-7824
IS - 4
ER -