The initial value problem for some hyperbolic-dispersive system

Abstract

We consider the initial value problem for some nonlinear hyperbolic-dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well-posedness for this system. We also discuss the extension of our results to more general hyperbolic-dispersive system. Copyright (C) 2011 John Wiley & Sons, Ltd.