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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 61, Pages 3275-3283
http://dx.doi.org/10.1155/S016117120431207X

On local smooth solutions for the Vlasov equation with the potential of interactions ±r2

Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Moscow region, Dubna 141980, Russia

Received 4 December 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

For the initial value problem for the Vlasov equation with the potential of interactions ±r2, we prove the existence and uniqueness of a local solution with values in the Schwartz space S of infinitely differentiable functions rapidly decaying at infinity.