March 1, 2004

Global Well-Posedness of the Benjamin–ono Equation in H1(r)

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Abstract

We show that the Benjamin–Ono equation is globally well-posed in H s (R) for s≥1. This is despite the presence of the derivative in the nonlinearity, which causes the solution map to not be uniformly continuous in H s for any s 18. The main new ingredient is to perform a global gauge transformation which almost entirely eliminates this derivative.

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Terence Tao (Mon,) studied this question.

synapsesocial.com/papers/69d95e875e5bcb4e3b835d59 https://doi.org/https://doi.org/10.1142/s0219891604000032

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