From the text: The authors study the Cauchy problem of the following generalized Davey-Stewartson systems:
where and are complex- and real-valued functions of , respectively, is the Laplace operator on , and , and are real constants. They study the local and global existence of solutions in . The main tools used are time-space estimates for solutions of linear Schrödinger equations in Lebesgue-Besov spaces; these estimates are usually named generalized Strichartz inequalities. The method of the proof of the main results is a contraction mapping argument.