Well-Posedness for the Schrödinger-Debye Equation
Felipe Linares | Corcho Fernandez, Adán
We establish local and global results for the initial value problem associated to the Schródinger-Debye system for data in low regularity spaces. The main tool used is an optimal application of the Strichartz estimates for the linear Schródinger operator. In the one dimensional case we also use Kato's smoothing effect to obtain global results in fractional Sobolev spaces.