On the propagation of regularities in solutions of the Benjamin-Ono equation

We shall deduce some special regularity properties of solutions to the IVP associated to the Benjamin-Ono equation. Mainly, for datum u(0) is an element of H-3/2(R) whose restriction belongs to H-m((b, infinity)) for some m is an element of Z(+), m >= 2, and b is an element of R we shall prove that the restriction of the corresponding solution u(., t) belongs to H-m ((beta, infinity)) for any beta is an element of R and any t > 0. Therefore, this type of regularity of the datum travels with infinite speed to its left as time evolves. (C) 2015 Elsevier Inc. All rights reserved.