Quadratic dispersive generalized Benjamin–Ono equation

This paper is concerned with quadratic dispersive generalized Benjamin–Ono equation (1.1)–(1.2). We prove sharp local well-posedness in H s α ( s α = − 1 + α 4 ) with a solution-map that is analytic from H s α ( R ) to C ( [ 0 , T ] ; H s α ( R ) ) . And the ill-posed result in H s ( R ) , as soon as s < s α , in the sense that the flow-map u 0 ↦ u ( t ) cannot be continuous.