Mathematical Research Letters

Volume 10 (2003)

Number 6

On the local well-posedness of the Benjamin-Ono and modified Benjamin-Ono equations

Pages: 879 – 895

DOI: http://dx.doi.org/10.4310/MRL.2003.v10.n6.a13

Authors

Carlos E. Kenig

Kenneth D. Koenig

Abstract

We prove that the Benjamin-Ono equation is locally well-posed in $H^s (\R)$ for $s > 9/8$ and that for arbitrary initial data, the modified (cubic nonlinearity) Benjamin-Ono equation is locally well-posed in $H^s (\ensuremath{{\bf R}})$ for $s \ge 1$.

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