Weak Continuity of the Flow Map for the Benjamin-Ono Equation on the Line
Analysis of PDEs
2009-10-08 v2
Abstract
In this paper we show that the floow map of the Benjamin-Ono equation on the line is weakly continuous in L2(R), using "local smoothing" estimates. L2(R) is believed to be a borderline space for the local well-posedness theory of this equation. In the periodic case, Molinet [27] has recently proved that the flow map of the Benjamin-Ono equation is not weakly continuous in L2(T). Our results are in line with previous work on the cubic nonlinear Schrodinger equation, where Goubet and Molinet [11] showed weak continuity in L2(R) and Molinet [28] showed lack of weak continuity in L2(T).
Keywords
Cite
@article{arxiv.0909.0793,
title = {Weak Continuity of the Flow Map for the Benjamin-Ono Equation on the Line},
author = {Shangbin Cui and Carlos E. Kenig},
journal= {arXiv preprint arXiv:0909.0793},
year = {2009}
}
Comments
34 pages, no figures. This new version modifies the previous one in accordance with the referee's comments