Global well-posedness for the Benjamin-Ono and intermediate long wave equations in L^2
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Abstract: In the first part of the talk, I will revisit the well-posedness theory of the Benjamin-Ono equation which has received a lot of attention in the past 20 years. In particular, I will explain the gauge transformation introduced by Tao in 2004, which was a breakthrough in order to attain lower regularities.
In the second part of the seminar, I will summarize a joint work with Luc Molinet published in 2012, where relying on the gauge transformation of Tao, we revisit the proof of the well-posedness in L^2 both on the line and on the torus (the result on R was obtained first by Ionescu and Kenig in 2007, while the one on T was proved by Molinet in 2008). Finally, I will explain how these ideas extend to perturbations of the Benjamin-Ono equation like the Intermediate Long Wave equation. This last result was obtained very recently in collaboration with Andreia Chapouto, Guopeng Li and Tadahiro Oh (University of Edinburgh).
