Local Well-Posedness for the Davey-Stewartson Equation in a Generalized Feichtinger Algebra

In this paper, we consider the initial value problem for the hyperbolic-type Davey-Stewartson equations, including elliptic-hyperbolic and hyperbolic-hyperbolic cases. We show the local existence and uniqueness of the solution in the generalized Feichtinger algebra with sufficiently small initial data in . Moreover, we show the ill-posedness of the solutions in the sense that the solution map is not if the spatial regularity is below .SCI(E)ARTICLEsugimoto@math.nagoya-u.ac.jp; wbx@pku.edu.cn; zhan1602@purdue.edu51105-11292