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 u0∈H3/2(R) whose restriction belongs to Hm((b,∞)) for some m∈Z+,m≥2, and b∈R we shall prove that the restriction of the corresponding solution u(⋅,t) belongs to Hm((β,∞)) for any β∈R and any t>0. Therefore, this type of regularity of the datum travels with infinite speed to its left as time evolves.