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.
|Number of pages||9|
|Journal||Mathematical Methods in the Applied Sciences|
|Publication status||Published - 2012 Jan 30|
- hyperbolic and dispersive system
- smoothing effect
ASJC Scopus subject areas