The Cauchy problem for the fourth-order Schrodinger equation in Hs

We consider the fourth-order Schrodinger equation i partial derivative(t)u + Delta(2)u + mu Delta u + lambda|u|(alpha)u = 0 in H-s(R-N), with N >= 1,lambda is an element of C, mu = +/- 1 or 0, 0 < s < 4, 0 < alpha, and (N - 2s)alpha < 8. We establish the local well-posedness result in H-s(R-N) by applying Banach's fixed-point argument in spaces of fractional time and space derivatives. As a by-product, we extend the existing H-2 local well-posedness results to the whole range of energy subcritical powers and arbitrary lambda is an element of C. Published under an exclusive license by AIP Publishing.