L2Global Well-Posedness of the Initial Value Problem Associated to the Benjamin Equation

We study well-posedness for the initial value problem associated to the Benjamin equation and the periodic Benjamin equation. Global results are established for data inL2( ) andL2( ), respectively. We apply the recent theory, developed by Kenig, Ponce, and Vega and Bourgain, to deal with low-regularity data for the initial value problem associated to the Korteweg-de Vries equation