On the Long Time Behavior of Solutions to the Intermediate Long Wave Equation

  title={On the Long Time Behavior of Solutions to the Intermediate Long Wave Equation},
  author={Claudio Mu{\~n}oz and Gustavo Ponce and Jean-Claude Saut},
  journal={SIAM J. Math. Anal.},
We show that the limit infimum, as time $\,t\,$ goes to infinity, of any uniformly bounded in time $H^{3/2+}\cap L^1$ solution to the Intermediate Long Wave equation converge to zero locally in an increasing-in-time region of space of order $\,t/\log(t)$. Also, for solutions with a mild $L^1$-norm growth in time is established that its limit infimum converge to zero, as time goes to infinity. This confirms the non existence of breathers and other solutions for the ILW model moving with a speed… Expand
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Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE
  • J. Saut
  • Physics, Mathematics
  • Nonlinear Dispersive Partial Differential Equations and Inverse Scattering
  • 2019
This survey article is focused on two asymptotic models for internal waves, the Benjamin-Ono (BO) and Intermediate Long Wave (ILW) equations that are integrable by inverse scattering techniquesExpand