N Hayashi   H Hirata   
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY 40(3) 563-581 1997年10月
We study the initial value problem to the Davey-Stewartson system for the elliptic-hyperbolic case in the usual Sobolev space. We prove local existence and uniqueness H-5/2 With a condition such that the L-2 norm of the data is sufficiently small.