The IVP for the Benjamin-Ono equation in weighted Sobolev spaces

@article{Fonseca2010TheIF,
  title={The IVP for the Benjamin-Ono equation in weighted Sobolev spaces},
  author={Germ{\'a}n E. Fonseca and Gustavo Ponce},
  journal={arXiv: Analysis of PDEs},
  year={2010}
}
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58 Citations
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References

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In a recent work, Ionescu and Kenig proved that the Cauchy problem associatedto the Benjamin-Ono equation is well-posed in $L^2(\mathbb R)$. In this paper we give a simpler proof of Ionescu and…
GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H1(R)
We show that the Benjamin–Ono equation is globally well-posed in Hs(R) for s≥1. This is despite the presence of the derivative in the nonlinearity, which causes the solution map to not be uniformly…
Well-posedness results for the generalized Benjamin-Ono equation with arbitrary large initial data
We prove new local well-posedness results for the generalized Benjamin-Ono equation (GBO) ∂tu+ℋ∂x2u+uk∂xu=0, k ≥ 2. By combining a gauge transformation with dispersive estimates, we establish the…
Benjamin–Ono Equation with Unbounded Data☆
Abstract The initial value problem (IVP) for the Benjamin–Ono equation with unbounded initial data is considered. We show existence and uniqueness of global solutions for sublinear growth data. The…
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Global well-posedness of the Benjamin-Ono equation in H^1(R)
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On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations
We prove that the Benjamin-Ono equation is locally well-posed in Hs(R) for s > 9/8 and that for arbitrary initial data, the modified (cubic nonlinearity) Benjamin-Ono equation is locally well-posed…
Ill-Posedness Issues for the Benjamin-Ono and Related Equations
We establish that the Cauchy problem for the Benjamin--Ono equation and for a rather general class of nonlinear dispersive equations with dispersion slightly weaker than that of the Korteweg--de…
On uniqueness properties of solutions of the k-generalized KdV equations
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