Averaging Lemmas and Dispersion Estimates for kinetic equations

Pierre-Emmanuel Jabin (1, 2)

1 TOSCA - Simuler et calibrer des modèles stochastiques
2 JAD - Laboratoire Jean Alexandre Dieudonné

Averaging lemmas consist in a regularizing effect on the average of the solution to a linear kinetic equation. Some of the main results are reviewed and their proofs presented in as self contained a way as possible. The use of kinetic formulations for the well posedness of scalar conservation laws is eventually explained as an example of application.

Mots clés: Regularizing effects; averaging lemmas; dispersion estimates; conservation laws

Domaines: Equations aux dérivées partielles [math.AP]; Algèbres d'opérateurs [math.OA]; Physique mathématique [math-ph]

Pierre-Emmanuel Jabin. Averaging Lemmas and Dispersion Estimates for kinetic equations. Rivista di Matematica della Università di Parma, 2009, 8 (1), pp.71-138. ⟨hal-00601944⟩