Weak Continuity of the Flow Map for the Benjamin-Ono Equation on the Line

Details Weak Continuity of the Flow Map for the Benjamin-Ono Equation on the Line Weak Continuity of the Flow Map for the Benjamin-Ono Equation on the Line

2009-09-04

arxiv.org/abs/0909.0793v2

Mathematics

Analysis of PDEs

34 pages, no figures. This new version modifies the previous one in accordance with the referee's comments

Scientific paper

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).

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