Global well posedness and scattering for the elliptic and non-elliptic derivative nonlinear Schrodinger equations with small data

Abstract

We study the Cauchy problem for the generalized elliptic and non-elliptic derivative nonlinear Schrodinger equations, the existence of the scattering operators and the global well posedness of solutions with small data in Besov spaces and in modulation spaces are obtained. In one spatial dimension, we get the sharp well posedness result with small data in critical homogeneous Besov spaces. As a by-product, the existence of the scattering operators with small data is also shown. In order to show these results, the global versions of the estimates for the maximal functions on the elliptic and non-elliptic Schrodinger groups are established.

43 pages

References in corpus (1)

• On the Cauchy- and periodic boundary value problem for a certain class of derivative nonlinear Schroedinger equations

Cited by in corpus (5)

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• Schrödinger Soliton from Lorentzian Manifolds
• Global well-posedness and scattering for Derivative Schrödinger equation