Global well-posedness of the Benjamin-Ono equation in H^1(R)

Details Global well-posedness of the Benjamin-Ono equation in H^1(R) Global well-posedness of the Benjamin-Ono equation in H^1(R)

2003-07-22

arxiv.org/abs/math/0307289v2

J. Hyperbolic Differential Equations 1 (2004) 27-49

Mathematics

Analysis of PDEs

21 pages, no figures. Minor mathematical errors corrected

Scientific paper

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 uniformly continuous in
$H^s$ for any $s$. The main new ingredient is to perform a global gauge
transformation which almost entirely eliminates this derivative.

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