Mathematical Research Letters

Volume 10, Issue 6, November 2003 pp. 879-895.

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

Authors: Carlos E. Kenig and Kenneth D. Koenig
Author institution: University of Chicago

Summary: 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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