International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 61-64, Pages 3275-3283
doi:10.1155/S016117120431207X

On local smooth solutions for the Vlasov equation with the potential of interactions ±r−2

Abstract

For the initial value problem for the Vlasov equation with the potential of interactions ±r−2, 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.