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Local existence in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system in the usual Sobolev space
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.