Averaging lemmas with a force term in the transport equation

✍ Scribed by F. Berthelin; S. Junca

• Book ID: 104044957
• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 248 KB
• Volume: 93
• Category: Article
• ISSN: 0021-7824
• DOI: 10.1016/j.matpur.2009.10.009

✦ Synopsis

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 2.