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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References

SHOWING 1-10 OF 66 REFERENCES
The Cauchy problem for the Benjamin-Ono equation in $L^2$ revisited
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
On well-posedness for the Benjamin–Ono equation
We prove existence and uniqueness of solutions for the Benjamin–Ono equation with data in $$H^{s}({\mathbb{R}})$$ , s > 1/4. Moreover, the flow is hölder continuous in weaker topologies.
Well-posedness for the Generalized Benjamin–Ono Equations with Arbitrary Large Initial Data in the Critical Space
We prove the local well-posedness of the generalized Benjamin-Ono equations , k ≥ 4, in the scaling invariant spaces where s k = 1/2 − 1/ k. Our results also hold in the nonhomogeneous spaces . In
Global well-posedness of the Benjamin-Ono equation in H^1(R)
We show that the Benjamin-Ono equation is globally well-posed in $H^s(\R)$ for $s \geq 1$. This is despite the presence of the derivative in the non-linearity, which causes the solution map to not be
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
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