Local well-posedness for third order Benjamin-Ono type equations on the torus

Abstract

We consider the Cauchy problem of third order Benjamin-Ono type equations on the torus. Nonlinear terms may yield derivative losses, which prevents us from using the classical energy method. In order to overcome that difficulty, we add a correction term into the energy. We also use the Bona-Smith type argument to show the continuous dependence.

23 pages, no figures

References in corpus (1)

• Higher order fractional Leibniz rule

Cited by in corpus (1)

• Local well-posedness for fourth order Benjamin-Ono type equations