On local energy decay for solutions of the Benjamin–Ono equation

We consider the long time dynamics of large solutions to the Benjamin–Ono equation. Using virial techniques, we describe regions of space where every solution in a suitable Sobolev space must decay to zero along sequences of times. Moreover, in the case of exterior regions, we prove complete decay for any sequence of times. The remaining regions not treated here are essentially the strong dispersion and soliton regions.