# 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}
}
• Published 30 April 2010
• Mathematics
• arXiv: Analysis of PDEs
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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
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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
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SIAM J. Math. Anal.
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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