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