On a Degenerate Zakharov System
Jean-Claude Saut | Linares, Felipe | Ponce, Gustavo
Zakharov systems | smoothing effects | Nonlinear Schrodinger equation
We establish a local well-posedness result for an initial value problem associated to a Zakharov system arising in in the study of laser-plasma interactions. We called this system degenerate due to the lack of dispersion presented in one of the spatial variables. One of the key tools to obtain our results is the presence of appropriate global versions of the so called ''local smoothing effects'' inherent to the dispersive character of the model.