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

Terence Tao

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

Terence Tao

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Abstract

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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Terence Tao. 2004-06-26. Global well-posedness of the Benjamin-Ono equation in H^1(R). https://arxiv.org/abs/math/0307289

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