Polynomial bound and nonlinear smoothing for the Benjamin-Ono equation on the circle

Academic Article


  • For initial data in Sobolev spaces Hs(T), [Formula presented], the solution to the Cauchy problem for the Benjamin-Ono equation on the circle is shown to grow at most polynomially in time at a rate [Formula presented], 0<ϵ≪1. The key to establishing this result is the discovery of a nonlinear smoothing effect for the Benjamin-Ono equation, according to which the solution to the equation satisfied by a certain gauge transform, which is widely used in the well-posedness theory of the Cauchy problem, becomes smoother once its free solution is removed.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Isom B; Mantzavinos D; Oh S; Stefanov A
  • Start Page

  • 25
  • End Page

  • 46
  • Volume

  • 297