Vol. 12, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 6, 1397–1642
Issue 5, 1149–1396
Issue 4, 867–1148
Issue 3, 605–866
Issue 2, 259–604
Issue 1, 1–258

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Ethics Statement
Author Index
To Appear
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Other MSP Journals
On propagation of higher space regularity for nonlinear Vlasov equations

Daniel Han-Kwan

Vol. 12 (2019), No. 1, 189–244

This work is concerned with the broad question of propagation of regularity for smooth solutions to nonlinear Vlasov equations. For a class of equations (that includes Vlasov–Poisson and relativistic Vlasov–Maxwell systems), we prove that higher regularity in space is propagated, locally in time, into higher regularity for the moments in velocity of the solution. This in turn can be translated into some anisotropic Sobolev higher regularity for the solution itself, which can be interpreted as a kind of weak propagation of space regularity. To this end, we adapt the methods introduced by D. Han-Kwan and F. Rousset (Ann. Sci. École Norm. Sup. 49:6 (2016) 1445–1495) in the context of the quasineutral limit of the Vlasov–Poisson system.

kinetic transport equations, kinetic averaging lemmas
Mathematical Subject Classification 2010
Primary: 35Q83
Received: 12 October 2017
Revised: 19 March 2018
Accepted: 19 April 2018
Published: 2 August 2018
Daniel Han-Kwan
École polytechnique