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Article Dans Une Revue Journal de Mathématiques Pures et Appliquées Année : 2010

Averaging lemmas with a force term in the transport equation

Florent Berthelin
Stéphane Junca

Résumé

We obtain several averaging lemmas for transport operator with a force term. These lemmas improve the regularity yet known by not considering the force term as part of an arbitrary right-hand side. Two methods are used: local variable changes or stationary phase. These new results are subjected to two non degeneracy assumptions. We characterize the optimal conditions of these assumptions to compare the obtained regularities according to the space and velocity variables. Our results are mainly in $L^2$, and for constant force, in $L^p$ for $1 < p \leq 2$.
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Dates et versions

hal-00874401 , version 1 (03-09-2019)

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Florent Berthelin, Stéphane Junca. Averaging lemmas with a force term in the transport equation. Journal de Mathématiques Pures et Appliquées, 2010, 93 (2), pp.113-131. ⟨10.1016/j.matpur.2009.10.009⟩. ⟨hal-00874401⟩
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